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Chapter 3 

Geometries with no orientation support 

 

84

 

Rockwell Automation Publication MOTION-UM002F-EN-P - February 2018 

Plan for singularity

 on 

page 86

 

Encounter a no-solution position

 on 

page 86

 

 

A robot having an arm configuration has two kinematics solutions when 
attempting to reach a given position. Point A is shown in the following 

illustration. One solution satisfies the equations for a right-armed robot, the other 

solution satisfies the equations for a left-armed robot. 

 

See also 

Arm solutions

 on 

page 83

 

For a three-dimensional Articulated Independent robot, there are four solutions 

for the same point: 

•

 

Left-arm 

•

 

Right-arm 

•

 

Left-arm mirror 

•

 

Right-arm mirror 

For example, consider the Cartesian point XYZ (10,0,15). The joint position 

corresponding to this point has four joint solutions. Two of the solutions are the 
same as the solutions for the two-dimensional case. The other solutions are mirror 
image solutions where J1 is rotated 180

.

 

Left-arm and right-arm 
solutions for two-axes robots 

Solution mirroring for 

three-dimensional robots 

Содержание 1756-M02AE

Страница 1: ...User Manual Motion Coordinate System 1756 HYD02 1756 M02AE 1756 M02AS 1756 M03SE 1756 M08SE 1756 M16SE 1768 M04SE ...

Страница 2: ...he contents of this manual in whole or in part without written permission of Rockwell Automation Inc is prohibited Throughout this manual when necessary we use notes to make you aware of safety considerations WARNING Identifiesinformationaboutpractices orcircumstancesthatcancause an explosionina hazardousenvironment which may leadto personal injury ordeath property damage or economic loss ATTENTIO...

Страница 3: ...n for the change and a link to the topic that contains the changed information Topic Name Reason Prefaceonpage 11 Updatedthe list ofmotioncoordinatedmotion applications to include instructionsthatsupport orientation Sample Projectsonpage11 Updatedthe default locationand how toaccess the PDF filethatexplains how toworkwithsample projects Generaltabonpage 22 Geometrytabonpage25 Units tabonpage26 Off...

Страница 4: ...configure the 3 axis robot geometrieswithno orientationsupport inLogix Designer forexample Articulate Independent and Dependent robots Delta Two and Three dimensional robots SCARA Delta and Independent robots and CartesianGantry and H bot robots Geometrieswithorientationsupport onpage115 New chapterthatprovides guidelines to configure robotgeometries withorientationsupport inLogix Designer forexam...

Страница 5: ...dinate System Properties dialog box Dynamics tab 29 Coordinate System Properties dialog box Dynamics tab parameters 30 Manual Adjust dialog box Dynamics tab 32 Coordinate System Properties dialog box Motion Planner tab 33 Coordinate System Properties dialog box Motion Planner tab parameters 33 Coordinate System Properties dialog box Tag tab 34 Coordinate System Properties dialog box Tag tab parame...

Страница 6: ...stablish a reference frame for an articulated dependent robot 78 Work envelope for articulated dependent robot 78 Configuration parameters for Articulated Dependent robot 79 Link lengths for Articulated Dependent robot 80 Base offsets for Articulated Dependent robot 81 End Effector Offsets for Articulated Dependent robot 82 Arm solutions 83 Left arm and right arm solutions for two axes robots 84 S...

Страница 7: ...a SCARA Independent Robot 107 Establish the reference frame for a SCARA Independent robot 107 Identify the work envelope for a SCARA Independent robot 109 Define configuration parameters for a SCARA Independent robot 109 Link lengths for SCARA Independent robot 110 Configure a Cartesian Gantry robot 111 Establish the reference frame for a Cartesian Gantry robot 111 Identify the work envelope for a...

Страница 8: ...entify the work envelope for Delta J1J2J3J6 robot 172 Maximum joint limit condition for Delta J1J2J3J6 robot 172 Work and Tool Frame offset limits for Delta J1J2J3J6 robot 174 Sample project for Delta J1J2J3J6 robot 175 Configure a Delta J1J2J3J4J5 Coordinate System 175 Establish the reference frame for a Delta J1J2J3J4J5 robot 177 Calibrate a Delta J1J2J3J4J5 robot 178 Configuration parameters fo...

Страница 9: ...le 218 Calculate a Cam Profile 218 Use Common Cam Profiles 219 Acceleration Cam Profile 219 Run Cam Profile 220 Deceleration Cam Profile 220 Dwell Cam Profile 221 Behavior of Pending Cams 222 Scaling cams 223 Scaling Position Cam Profile 223 Scaling Time Cam Profiles 224 Cam Execution Modes 225 Execution Schedule 226 Execution Schedule for the MAPC Instruction 226 Execution Schedule for the MATC I...

Страница 10: ......

Страница 11: ...porates translationandorientationinitspositiontransformation MotionCoordinatedTransformwithOrientation MCTO 2 Calculatethe positionofone coordinate systemwithrespecttoanothercoordinatesystem MotionCalculate Transform Position MCTP 1 Calculatethe positionof apoint inone coordinate system to the equivalent point ina second coordinate system MotionCoordinatedTransform PositionwithOrientation MCTPO 2 ...

Страница 12: ...System UserManual publication1756 UM001 Describesthe necessary tasks to install configure program andoperatea ControlLogix system ControlLogix5580 andGuardLogix5580Controllers UserManual publication 1756 UM543 Provides completeinformationonhowtoinstall configure select I Omodules manage communication develop applications and troubleshoot theControlLogix 5580and GuardLogix5580 controllers CompactLo...

Страница 13: ...ut us contact contact page Please include Open Source as part of the request text The following open source software is used in this product Software Copyright License Name License Text AngularJS Copyright2010 2017Google Inc MITLicense AngularJS1 5 9License Bootstrap Copyright2011 2017 Twitter Inc Copyright2011 2017 TheBootstrapAuthors MITLicense Bootstrap3 3 7 License jQuery Copyright2005 2014 JS...

Страница 14: ... hereby acknowledged Warranty This product is warranted in accordance with the product license The product s performance may be affected by system configuration the application being performed operator control maintenance and other related factors Rockwell Automation is not responsible for these intervening factors The instructions in this document do not cover all the details or variations in the...

Страница 15: ...Preface Rockwell AutomationPublicationMOTION UM002F EN P February2018 15 Contact Rockwell Customer Support Telephone 1 440 646 3434 Online Support http www rockwellautomation com support ...

Страница 16: ......

Страница 17: ...ed to generate coordinated motion The Logix Designer application supports the following geometry types Cartesian Articulated Dependant Articulated Independent Selective Compliant Assembly Robot Arm SCARA Independent Delta SCARA Delta The following are coordinate system examples Coordinate system with orthogonal axes Cartesiancoordinatesystem Two dimensional Cartesiancoordinate system Three dimensi...

Страница 18: ...culated Dependent coordinatesystem Articulated Independent coordinatesystem SCARA Independent coordinatesystem Delta Two dimensional coordinate system Delta Three dimensional coordinate system SCARA Delta coordinate system DeltaJ1J2J6 coordinatesystem DeltaJ1J2J3J6 coordinate system DeltaJ1J2J3J4J5 coordinate system See also Create a coordinate system on page 19 ...

Страница 19: ...ons The Coordinate System tag Defines the COORDINATE_SYSTEM data type Associates the Coordinate System to a Motion Group Associates the axes to the Coordinate System Sets the dimension Defines the values used by the operands of the Multi Axis Motion Instructions Configuring the Coordinate System tag defines the values for Coordination Units Maximum Speed Maximum Acceleration Maximum Deceleration A...

Страница 20: ... create For a coordinate system the only valid choices are Base Refers to a normal tag and is the default Alias Refers to a tag that references another tag with the same definition 5 In the Data Type box select COORDINATE_SYSTEM 6 In the External Access box select whether the tag has None Read Write or Read Only access from external applications such as HMIs 7 Select the Constant check box to prev...

Страница 21: ...he Coordinate System properties 1 In the Controller Organizer expand the Motion Group folder and double click the Coordinate System or right click the Coordinate System and select Properties 2 Use the tabs in the Coordinate System Properties dialog box to make the appropriate changes An asterisk appears on the tab to indicate that changes have been made but not implemented 3 Click Apply to save th...

Страница 22: ...d PositionTolerance andOrientationvalues fora Cartesian coordinate system Joints The Jointstab defines the Joints Conversionratios MotionPlanner The MotionPlanner tabenablesordisablesMasterDelay CompensationorMasterPositionFilter Tag The Tag tab is used to renamethetag editthe description and review theTag Type Data Type and Scope information See also Coordinate System Properties dialog box Genera...

Страница 23: ...n Group select the coordinate system type and enter associated axis information Tip The Type selectiondeterminesthe tabs available inthe CoordinateSystem Properties dialog box Parameter Description MotionGroup The MotionGroupassociatedwiththe CoordinateSystem A CoordinateSystemassignedto aMotionGroup is displayed inthe MotionGroupsfolderinthe Controller Organizer underthe selectedMotionGroup sub f...

Страница 24: ...motioninstructions map toaxesusing these indices Coordinate Displaysthe cross reference to the axes inthe grid AxisName Associates anaxistagtothe coordinate The defaultis none The list displaystheBase Tag axes definedinthe project Alias Tag axes do not display inthe list The tags canbe axes associatedwiththemotiongroup axesassociatedwithothercoordinated systems or axesfrom the Ungrouped Axes folde...

Страница 25: ...he Geometry tab in the Coordinate System Properties dialog box define the dimensional characteristics for the robotic geometry type to configure key The graphic displayed on the tab shows a typical representation of the type of coordinate system selected on the General tab Your robot typically looks similar to the one shown in the graphic but can be different depending on the application The setti...

Страница 26: ...nfigurationis determined bythe geometry type and coordinate definitionenteredontheGeneraltab ZeroAngleOrientation The rotational offsetofthe individual joint axes If applicable entertheoffset valueindegrees foreach joint axis The numberofangle identifiers available forconfigurationis determined bythe geometry typeand coordinate definitionenteredontheGeneraltab See also Coordinate System Properties...

Страница 27: ...toraninteger The denominatormust be entered asan integeronly ConversionRatio Units Displaysthe axis positionunits to coordinationunits used The coordinationunits are defined intheCoordinationUnitsparameteronthistab The Axis Position units are defined onthe Unitstab inthe AxisPropertiesdialog box These values are dynamically updatedwhenchanges aremade toeitheraxis positionunitsorcoordinationunits S...

Страница 28: ...n The difference betweenthesetwo locations isthe baseoffset values The correct baseoffset values are typically availablefrom the robotmanufacturer The baseoffset indicators areX1b X2band X3bwhenthe CoordinationDefinitionis none Baseand EffectorPlateDimensions Rb indicates the Base plate radius andReindicates the End Effectorplate radius This parameterisavailableonly whentheGeometry Typeis Deltaand...

Страница 29: ...sionenteredonthe Generaltab AxisName The nameof axis associatedwiththe coordinate system The namesappears intheorderthat theywere configured inthe coordinate system JointRatio Defines therelationship betweenthe axis positionunits and degrees The JointRatiois divided into two fields The left halfofthe JointRatio columnis used to specify the numeratorvalueof Joint Positionunits perdegreeforeachjoint...

Страница 30: ...culations when the operands are expressed as percent of Maximum The Coordination Units automatically change when the coordination units are redefined on the Units tab The Orientation values are used by the Motion Coordinate Path Move MCPM instruction These values are always in units of degrees and only available when System Type is Cartesian and Coordinate Definition is none Parameter Description ...

Страница 31: ...onaredefined as MaxDecel2 Speed MaximumDecelerationJerk This value is usedwhenthemotioninstructionisset withJerkUnits ofMaximum WhenaMulti axismotioninstructionhas JerkUnits units persec3 thentheMax Deceleration Jerkvalue is derived fromtheMotionInstructionfaceplate The jerkunitsforthemotion instructionalsoallow forJerkUnits of Time with100 of Timemeaningthe entire S curve movewill have Jerklimiti...

Страница 32: ...ocalculate vectorspeedwhenspeed is expressed as a percent ofmaximum VectorMaximumAcceleration The value usedby theCoordinated Motioninstructionstodetermine theaccelerationrateto apply tothe coordinate system vectorwhenaccelerationis expressed asa percentof maximum VectorMaximum Deceleration The value usedby theCoordinated Motioninstructionstodetermine thedecelerationrate to apply tothe coordinate ...

Страница 33: ...diately resetwhen clicking Reset See also Coordinate System Properties dialog box Dynamics tab parameters on page 30 How do I open the Motion Planner tab 1 In the Controller Organizer expand the Motion Group folder and double click the coordinate system 2 On the Coordinate System Properties dialog box click the Motion Planner tab Use this settings on the Motion Planner tab in the Coordinate System...

Страница 34: ...there is no need to compensate formasterpositiondelay Enable MasterPositionFilter Determineswhethertoenableordisable MasterPositionFilter The MasterPositionFilterfilters thespecifiedmasteraxis positioninputto theslaveaxis s gearing orpositioncamming operation The filtersmoothsout theactual positionsignal from theMasterAxis and thus smooths outthe correspondingmotionoftheSlaveAxis Selectthe checkbo...

Страница 35: ...rdinate Systemtags canbe eithera baseoranalias tag DataType The datatypeofthe CoordinateSystem tag Scope Displaysthe scopeofthe CoordinateSystemtag CoordinateSystem tags canonly be controllerscope tags Class Displaysthe classofthe CoordinateSystem tag Coordinate System tags canonly be a Standard class External Access Displayswhetherthe CoordinateSystem tag hasRead Write Read Only ornoaccess NONE f...

Страница 36: ...y2018 Cartesian none 3 Configurea CartesianGantry robot onpage111 Cartesian XYZRxRyRz 6 Configurea CartesianXYZRxRyRz CoordinateSystemonpage39 Articulated Dependent none 2 or3 ConfigureanArticulated Dependent robotonpage 75 Articulated Independent none 2 or3 Configuring anArticulated Independent robotonpage 65 ...

Страница 37: ...onMOTION UM002F EN P February2018 37 SCARA Independent none 2 Configurea SCARAIndependenton page107 Delta none 2 Configurea Delta Two dimensional robotonpage96 Delta none 3 Configurea Delta Three dimensional robotonpage 87 Delta J1J2J6 3 Configuring aDelta J1J2J6 roboton page147 ...

Страница 38: ...tionMOTION UM002F EN P February2018 Delta J1J2J3J6 4 Configuring aDelta J1J2J3J6 robot onpage161 Delta J1J2J3J4J5 5 Configurea Delta J1J2J3J4J5robot onpage175 SCARA Delta none 2 Configuring aSCARA Delta robot onpage102 See also Coordinate System Properties dialog boxes on page 21 ...

Страница 39: ...hese guidelines to configure a Cartesian coordinate system in the Coordinate System Properties dialog box General tab On the General tab select Cartesian as the coordinate system type There are two Coordination Definitions available for a Cartesian coordinate system none XYZRxRyRz Select none to configure the Cartesian coordinate system without orientation support and then select the Dimension and...

Страница 40: ...dinate system with orientation support The Dimension and Transform Dimension values are automatically set to 6 and are unavailable to modify The Coordinate column displays the World Cartesian Coordinate names X Y and Z for the Primary axes and Rx Ry and Rz for the Orientation axes Rx is the rotation around the X axis Ry is the rotation around the Y axis and Rz is the rotation around the Z axis wit...

Страница 41: ...e parameters depend on the Transform Dimension value Tip The Base Offsetsand End Effector Offsetsparametersare unavailable if the Coordinate Definitionis XYZRxRyRz Dynamics tab The Dynamics tab is only valid for a Cartesian coordinate system Use the tab to configure the orientation values required for the Motion Coordinated Path Move MCPM instruction Orientation Maximum Speed Orientation Maximum A...

Страница 42: ...nstructionto start asingleormulti dimensional linearcoordinated moveforthe specifiedaxeswithina Cartesiancoordinate system MotionCoordinatedCircularMove MCCM Use theMCCMinstructionto initiate atwoorthree dimensional circularcoordinatedmove for the specifiedaxeswithina Cartesiancoordinatesystem MotionCoordinatedTransform MCT Use theMCTinstructionto starta transform that links two coordinatesystems ...

Страница 43: ...s1 to blend Move1 into Move2 See also Example ladder diagram for blended instructions on page 43 If Step 1 then Move1 starts and moves the axes to a position of 5 0 and once Move1 is in process and there is room to queue another move then Step 2 If Step 2 then Move1 is already happening Move2 goes into the queue and waits for Move1 to complete When Move1 is complete Move2 moves the axes to a posit...

Страница 44: ...nis pending inthe queue MovePendingStatus bit 1 MovePendingQueueFullStatus bit 1 You cannot queue anotherinstruction Anactive instructioncompletesand leaves thequeue MovePendingStatus bit 0 MovePendingQueueFullStatus bit 0 You canqueue anotherinstruction The termination type operand for the MCLM or MCCM instruction specifies how the currently executing move gets terminated These illustrations show...

Страница 45: ...a Cartesianand a robot systemswithcoordinatesthat are jointaxes of a robot The XYZ translationcoordinatesand the RxRyRz orientationcoordinates inthefixedangle conventiondefine theCartesiancoordinates MotionCalculate Transform PositionwithOrientation MCTPO Use theMCTPO instructionto calculate the positionof apoint inone coordinatesystem tothe equivalentpoint ina second coordinate system See the Log...

Страница 46: ...lending throughtheBlending TerminationType6 The otherblendingterminationtypes TerminationTypes2 and3 are not supportedfor the MCPM instruction The TerminationTypeforMCPMis specified via the PATH_DATAmembervariable TerminationType The Cartesianpositionwhere blending should start is specified inthePATH_DATA structurememberCommandToleranceLinear Fororientationpathblending there is noequivalent progra...

Страница 47: ... pathlengthis reserved forblending Intheexampleshown MCPM1 is a TT6orientation only movewitha queuedMCPM2 TT6 orientation only move TheMCPM1move isa startingmove but endmove is unknown therefore50 ofthemove lengthis reserved forblending See also Choose a termination type on page 55 Use MCPM blending with orientation to synchronize Cartesian path and orientation motion on page 47 The following is a...

Страница 48: ...ange by 50 0 by the end of the move trajectory The orientation is prohibited from moving for the first 200 millimeters of move 1 and also prohibited from moving the final 250 millimeters Move 1 PATH_DATA Move 2 PATH_DATA Move 3 PATH_DATA The vertical moveis configuredwithterminationtype 6and the desired command tolerance The horizontalmove also isterminationtype 6withcommand tolerance The final ve...

Страница 49: ...s Motion Instructions Reference Manual publication MOTION RM002 See also Choose a termination type on page 55 Blending Path Move with MCPM on page 45 Use the superimposed move feature to superimpose multiple moves instructions on a single axis This feature synchronizes a robot s motion with other parts of the application for example conveyor tracking and vision systems As shown in the illustration...

Страница 50: ...delta robot In this example the conveyor axis is a Master axis which commands the slave axis X The Conveyor axis is moved using a MAJ instruction When the MCPM instruction is executed the X position on the path point is added to the X axis position output from the MAG which is an input into MCTO MCTO outputs joint values for the robot there by tracking the object on the conveyor belt The applicati...

Страница 51: ...using actual tolerance or no settle on page 53 Bit States at transition points of blended move by using no decel on page 52 Bit states at transition points of blended move by using command tolerance on page 53 Bit states at transition points of blended move by using follow contour velocity constrained or unconstrained on page 54 This topic lists the bit states at transition points of Blended Move ...

Страница 52: ...sition points of blended move by using no decel linear linearmove This table shows the bit status at the various transition points shown in the preceding graph with termination type of No Decel For No Decel termination type distance to go for transition point TP2 is equal to deceleration distance for the Move1 instruction If Move 1 and Move 2 are collinear then Move1 PC will be true at TP3 which i...

Страница 53: ...tes at transition points of Blended Move by using Command Tolerance linear linearmove This table shows the bit status at the various transition points shown in the preceding graph with termination type of Command Tolerance For Command Tolerance termination type distance to go for transition point TP2 is equal to Command Tolerance for the coordinate system cs1 Bit TP1 TP2 TP3 TP4 Move1 DN T T T T M...

Страница 54: ...ransition points of blended move by using follow contour velocity constrained or unconstrained linear circularmove This table shows the bits status at the transition points Bit TP1 TP2 TP3 Move1 DN T T T Move1 IP T F F Move1 AC T F F Move1 PC F T T Move2 DN T T T Move2 IP T T F Move2 AC F T F Move2 PC F F T cs1 MoveTransitionStatus F F F cs1 MovePendingStatus T F F cs1 MovePendingQueueFullStatus T...

Страница 55: ...nd positionequalstarget position The vectordistance betweenthetarget and actual positions is lessthanorequal tothe Actual PositionToleranceofthe Coordinate System 0 Actual Tolerance The command positionequalsthe targetposition 1 No Settle keep thespeedconstant except betweenmoves The command positiongetswithinthe Command PositionTolerance of the coordinatesystem 2 Command Tolerance The axes gettot...

Страница 56: ...anorequaltotheActual Position Tolerance of the coordinatesystem Atthat point the instructioniscomplete and aqueued MCLMorMCCM instructioncanstart Important Makesure that you set the Actual Tolerance to a valuethat youraxes canreach Otherwise the instructionstays inprocess 1 No Settle The instructionstaysactiveuntil the command position equals the target position Atthat point the instruction is com...

Страница 57: ...mmand Tolerance lengthused for eachindividual instruction TerminationType Example Path Description 3 No Decel The instructionstaysactiveuntil the axes get tothe decelerationpoint At that point the instructionis completeand a queuedMCLMorMCCM instructioncan start The decelerationpoint dependsonwhetheryou use a trapezoidalorS curve profile If you don t have aqueued MCLMorMCCM instruction the axes st...

Страница 58: ...deviate from the path that you would have seen if the move had not been stopped and resumed The same phenomenon can occur if the move is within the decel point of the start of the blend In either case the deviation will most likely be a slight deviation Velocity Profiles for Collinear Moves Collinear moves are those that lie on the same line in space Their direction can be the same or opposite The...

Страница 59: ...e point the move is over and the PC bit is set Velocity Profile of Two Collinear Moves When the Second Move has a Higher Velocity than the First Move and Termination Type 2 or 6 is Used Velocity Profiles for Collinear Moves with Termination Types 3 4 or 5 This illustration shows a velocity profile of two collinear moves The second MCLM instruction has a lower velocity than the first MCLM instructi...

Страница 60: ...y Unconstrained 5 The PC bit is set when the first move reaches its programmed endpoint Velocity Profile of Two Collinear Moves When the Second Move has a Higher Velocity than the First Move and Termination Type 3 4 or 5 is Used Symmetric Profiles Profile paths are symmetric for all motion profiles Programming the velocity acceleration and deceleration values symmetrically in the forward and rever...

Страница 61: ...ic you must terminate any sequence of moves by either Termination Types 0 or 1 You should also use a Termination Type of 0 or 1 at the Reversal Point of a profile that moves back on itself Using a TT2 TT3 TT4 TT5 ot TT6 as the last move in a profile or the reversal point is safe However the resulting trajectory from A to B may not always be the same as that from B to A Explicit termination of the ...

Страница 62: ...and place action in four moves minimize the Jerk rate and use a triangular velocity profile Then use termination type 5 The other termination types may not let you get to the speed you want TerminationTypes2 3 4 or 6 The lengthof eachmove determines itsmaximum speed As aresult the axeswill not reacha speedthat causes themto overshootthe target positionduring deceleration ...

Страница 63: ... deceleration halfofthe profile Blending Moves at Different Speeds You can blend MCLM and MCCM instructions where the vector speed of the second instruction is different from the vector speed of the first instruction If the next move is And the TerminationType of the first move is Then Slower 2 Command Tolerance 3 No Decel 4 ContourVelocity Constrained 5 ContourVelocity Unconstrained 6 Command Tol...

Страница 64: ...esiancoordinatesystem 64 Rockwell AutomationPublicationMOTION UM002F EN P February2018 Faster 2 Command Tolerance 3 No Decel 6 Command ToleranceProgrammed 4 ContourVelocity Constrained 5 ContourVelocity Unconstrained ...

Страница 65: ... Coordinate System Properties dialog box determines whether or not there is orientation support in the coordinate system See also Configure a Cartesian Coordinate System on page 39 Use these guidelines when configuring an Articulated Independent robot Beforeturning ONthe Transformand orestablishing the reference frame be sureto dothe following forthe jointsof the target coordinate system Setand en...

Страница 66: ...sitions Failure to properly establishthecorrect reference frame foryourrobot cancausethe roboticarmtomovetounexpected positions causingmachine damage and orinjury or deathto personnel The reference frame for an Articulated Independent robot is located at the base of the robot as shown in this figure Illustration 1 Before establishing the Joint to Cartesian reference frame relationship it is import...

Страница 67: ...ne J2 is measured counterclockwise starting with J2 0 when L1 is parallel to X1 X2 plane J3 is measured counterclockwise with J3 0 when L2 is aligned with link L1 When the robot is physically in this position the Logix Designer application Actual Position tags for the axes must be J1 0 J2 0 J3 0 Illustration 3 Side view When the robot is physically in the above position the Logix Designer applicat...

Страница 68: ...d prior to programming a Motion Redefine Position MRP instruction and want these travel limits to stay operational Method 2 Uses a MRP instruction to redefine the axes position to align with the joint reference frame This method may require the soft travel limits to be adjusted to the new reference frame See also Method 1 for an incremental axis on page 68 Method 2 for an absolute axis on page 69 ...

Страница 69: ...tem Propertiesdialog box to J1 10 J2 80 J3 5 Z1 10 Z2 10 Z3 5 The Joint to Cartesian reference frame relationship is automatically established by the Logix controller after the Joint coordinate system parameters link lengths base offsets and end effector offsets are configured and the MCT instruction is enabled See also Methods to establish a reference frame on page 68 Position the robot so that L...

Страница 70: ...rientation on page 68 The work envelope is the three dimensional region of space that defines the reaching boundaries for the robot arm The work envelope for an articulated robot is ideally a complete sphere with an inner radius equal to L1 L2 and outer radius equal to L1 L2 Due to the range of motion limitations on individual joints the work envelope may not be a complete sphere If the range of m...

Страница 71: ... on page 65 Configure the Logix Designer application to control robots with varying reach and payload capacities The configuration parameter values for the robot include Link lengths Base offset End effector offsets The configuration parameter information is available from the robot manufacturer Important Verify thatthe values fortheLink Lengths Base Offsets and End Effector Offsetsare entered in ...

Страница 72: ... 72 Base offsets for Articulated Independent robot on page 73 End effector offsets for Articulated Independent robot on page 74 Link lengths are the rigid mechanical bodies attached at joints For anarticulated independent robot with The lengthof Isequal tothe value of the distance between 2 dimensions L1 L2 J1 and J2 J2 andthe end effector 3 dimensions L1 L2 J2 and J3 J3 andthe end effector Link l...

Страница 73: ...fector offsets for Articulated Independent robot on page 74 Configuration parameters for Articulated Independent robot on page 71 The base offset is a set of coordinate values that redefines the origin of the robot The correct base offset values are typically available from the robot manufacturer Type the values for the Base Offsets in the X1b and X3b boxes on the Geometry tab in the Coordinate Sy...

Страница 74: ...Articulated Independent robots on page 71 The robot can have an end effector attached to the end of robot link L2 If there is an attached end effector configure the End Effector Offset value on the Offsets tab in the Coordinate System Properties dialog box The End Effector Offsets are defined with respect to the tool reference frame at the tool tip End Effector Offsets for Articulated Independent ...

Страница 75: ...3 The Articulated dependent robot contains motors for the elbow and the shoulder at the base of the robot The dependent link controls J3 at the elbow Follow these guidelines when configuring an Articulated Dependent robot Beforeturning ONthe Transformand orestablishing the reference frame do the following forthe jointsofthe target coordinate system Setand enable thesofttravel limits Enable the har...

Страница 76: ...e damageand orinjury ordeathto personnel Example 1 Articulated Dependent robot 1 This diagram illustrates the reference frame for an Articulated Dependent robot at the base of the robot These equations represent the Articulated Dependent robot joint positioning shown in Articulated Dependent robot 1 diagram J1 is measured counterclockwise around the X3 axis starting at an angle of J1 0 when L1 and...

Страница 77: ...be J1 0 J2 90 J3 90 Example 3 ArticulatedDependent3 If the position and joint angle values of the robot are unable to match the Articulated Dependent 2 or in Articulated Dependent 3 examples use a methods outlined in the Method to Establish a Reference Frame for an articulated dependent robot topic to establish the Joint to Cartesian reference frame relationship See also Methods to establish a ref...

Страница 78: ...struction and want these travel limits to stay operational Method 2 Uses a MRP instruction to redefine the axes position to align with the joint reference frame This method may require the soft travel limits to be adjusted to the new reference frame See also Method 1 Establish a reference frame on page 68 Method 2 Establish a reference frame using a MRP instruction on page 69 The work envelope is ...

Страница 79: ...heenvelope of the tool centerpoint sweep inJ2 and J3while J1remains ata fixed positionof 0 See also Configuration parameters for Articulated Dependent robot on page 79 Articulated dependent robot on page 75 Configure the Logix Designer application to control robots with varying reach and payload capacities Be sure to have these configuration parameter values for the robot Link lengths Base offsets...

Страница 80: ...e X3b and X3e are X2b and X2e See also Link lengths for Articulated Dependent robot on page 80 Base offsets for Articulated Dependent robot on page 81 End Effector Offsets for Articulated Dependent robot on page 82 Link lengths are the rigid mechanical bodies attached at joints For anarticulated dependent robot with The lengthof Isequal tothe value of the distance between 2 dimensions L1 L2 J1 and...

Страница 81: ...e 79 End Effector Offsets for Articulated Dependent robot on page 82 Base offsets for Articulated Dependent robot on page 81 The Base Offsets are a set of coordinate values that redefine the origin of the robot The correct base offset values are typically available from the robot manufacturer Type the values for the Base Offsets in the X1b and X3b boxes on the Geometry tab in the Coordinate System...

Страница 82: ...n page 80 End Effector Offsets for Articulated Dependent robot on page 82 The robot can have an end effector attached to the end of robot link L2 If there is an attached end effector configure the End Effector Offset value on the Offsets tab in the Coordinate System Properties dialog box The End Effector Offsets are defined with respect to the tool reference frame at the tool tip End Effector Offs...

Страница 83: ...sets for Articulated Dependent robot on page 81 A kinematic arm solution is the position of all joints on the robot that correspond to a Cartesian position When the Cartesian position is inside the workspace of the robot then at least one solution always exists Many of the geometries have multiple joint solutions for a single Cartesian position Two axis robots two joint solutions typically exist f...

Страница 84: ...lution satisfies the equations for a left armed robot See also Arm solutions on page 83 For a three dimensional Articulated Independent robot there are four solutions for the same point Left arm Right arm Left arm mirror Right arm mirror For example consider the Cartesian point XYZ 10 0 15 The joint position corresponding to this point has four joint solutions Two of the solutions are the same as ...

Страница 85: ...3 You can switch the robot from a left arm solution to a right arm solution or vice versa This is done automatically when a joint move is programmed forcing a left right change to occur After the change is performed the robot stays in the new arm solution when Cartesian moves are made If required the robot arm solution changes again when another joint move is made Changethe robot armsolution ...

Страница 86: ...f a singularity is dependent on the type of the robot geometry and the size of the link lengths for the robot Not all robot geometries have singularity positions For example singularities for an Articulated Independent robot occur when The robot manipulator folds its arm back onto itself and the Cartesian position is at the origin The robot is fully stretched at or very near the boundary of its wo...

Страница 87: ...s on page 83 The Logix Designer application supports three types of geometries that are often called parallel manipulators Three dimensional Delta Two dimensional Delta SCARA Delta In these geometries the number of joints is greater than the degrees of freedom and not all the joints are actuated motor driven These un actuated joints are typically spherical joints See also Configure a Delta Three d...

Страница 88: ...1 X2 X3 direction The gripper remains vertical along the X3 axis while its position is translated to X1 X2 X3 space by the mechanical action of the parallelograms in each of the forearm assemblies The mechanical connections of the parallelograms via spherical joints ensures that the top and bottom plates remain parallel to each other Program the TCP to an X1 X2 X3 coordinate then the Logix Designe...

Страница 89: ... up out of the paper See also Calibrate a Delta Three dimensional robot on page 89 Use these steps to calibrate the robot To calibrate a Delta Three dimensional robot 1 Obtain the angle values from the robot manufacturer for J1 J2 and J3 at the calibration position Use these values to establish the reference position 2 Move all joints to the calibration position by jogging the robot under programm...

Страница 90: ... robot geometries the internal transformation equations in the Logix Designer application are written assuming that Joints are at 0 when link L1 is horizontal As each top link L1 moves downward its corresponding joint axis J1 J2 or J3 is rotating in the positive direction If you want the joint angular position when L1 is horizontal to be at any other value than 0 then configure the zero angle orie...

Страница 91: ...egion with sides similar to a hexagonal prism and the lower portion similar to a sphere For more information regarding the work envelope of Delta three dimensional robots see the documentation provided by the robot manufacturer Program the robot within a rectangular solid defined inside the robot s work zone The rectangular solid is defined by the positive and negative dimensions of the X1 X2 X3 v...

Страница 92: ... Properties dialog box Geometry and Offsets tabs During each scan the joint positions in the forward and inverse kinematics routines are checked to ensure that they are within the maximum and minimum negative joint limits Homing or moving a joint axis to a position beyond a computed joint limit and invoking a MCT instruction results in an error 67 Invalid Transform position For more information re...

Страница 93: ... absolute value of X1b X1e The derivations for the maximum negative joint limit applies to the condition when L1 and L2 are folded back on top of each other R is computed by using the base and end effector offsets values X1b and X1e Maximum negative joint limit condition R absolute value of X1b X1e JMaxNeg cos 1 Maximumnegative joint limit condition ...

Страница 94: ...sing the samemeasurement units See also Link Lengths for Delta Three dimensional robot on page 94 Base Offsets for Delta Three dimensional robot on page 95 End Effector offsets for Delta Three dimensional robot on page 95 Link lengths are the rigid mechanical bodies attached at the rotational joints The three dimensional Delta robot geometry has three link pairs made up of L1 and L2 Each of the li...

Страница 95: ...n of the robot coordinate system to one of the actuator joints Enter the base offset value for the three dimensional Delta robot on the Offset tab in the Coordinate System Properties dialog box See also Define configuration parameters for a Delta Three dimensional robot on page 94 The two End Effector Offsets available for the three dimensional Delta robot geometry are X1e This is the distance fro...

Страница 96: ...lta Three dimensional robot on page 95 This illustration shows a two dimensional Delta robot that moves in two dimensional Cartesian space This robot has two rotary joints that move the gripper in the X1 X2 plane Two forearm assemblies attach a fixed top plate to a movable bottom plate A gripper is attached to the movable bottom plate The bottom plate is always orthogonal to the X2 axis and its po...

Страница 97: ...or rotary independent axis See also Establish the reference frame for a Delta Two dimensional robot on page 97 Calibrate a Delta Two dimensional robot on page 98 Identify the work envelope for a Delta Two dimensional robot on page 98 Define configuration parameters for a Delta Two dimensional robot on page 99 The reference frame for the two dimensional Delta geometry is located at the center of th...

Страница 98: ...lta robot within a rectangle dotted lines in the illustration inside the robots work zone Define the rectangle by the positive and negative dimensions of the X1 X2 virtual source axes Be sure that the robot position does not go outside the rectangle Check the position in the event task To avoid problems with singularity positions the Logix Designer application internally calculates the joint limit...

Страница 99: ...bot include Link lengths Base offsets End effector offsets The configuration parameter information is available from the robot manufacturer Important Verify thatthe values fortheLink Lengths Base Offsets and End Effector Offsetsare entered inthe Coordinate System Properties dialogboxusing the samemeasurement units See also Link Lengths for Delta Two dimensional robot on page 100 Base Offset for De...

Страница 100: ...on page 99 The X1b base offset value is available for the two dimensional Delta robot geometry Enter a value equal to the distance from the origin of the robot coordinate system to one of the actuator joints Enter the base offset value for the two dimensional Delta robot on the Offset tab in the Coordinate System Properties dialog box BaseOffsets for Delta Two dimensional robot ...

Страница 101: ...imensional Delta robot geometry X1e This is the offset distance from the center of the lower plate to the lower spherical joints of the parallel arms X2e This is the distance from the lower plate to the TCP of the gripper Enter the end effector offset values on the Offsets tab in the Coordinate System Properties dialog box See also Define configuration parameters for a Delta Two dimensional robot ...

Страница 102: ...0 the two L1 links is along the X1 axis One L1 link is pointing in the positive X1 direction the other in the negative X1 direction When the right hand link L1 moves in the clockwise direction looking down on the robot joint J1 is assumed to be rotating in the positive direction When the right hand link L1 moves counterclockwise joint J1 is assumed to be moving in the negative direction When left ...

Страница 103: ... linear axis extends the work region making it a solid region The maximum positive and negative limits of the linear axis defines the height of the solid region It is recommended to program the SCARA Delta robot within a rectangular solid defined inside the work zone of the robot Define the rectangular solid by the positive and negative dimensions of the X1 X2 X3 virtual source axes Be sure that t...

Страница 104: ...cturer Important Verify thatthe values fortheLink Lengths Base Offsets and End Effector Offsetsare entered inthe Coordinate System Properties dialogboxusing the samemeasurement units See also Link length for SCARA Delta robot on page 105 Base Offset for SCARA Delta robot on page 105 End Effector Offset for SCARA Delta robot on page 105 Links are the rigid mechanical bodies attached at joints The S...

Страница 105: ...from the center of the moving plate to one of the spherical joints of the parallel arms The End Effector Offsets value is always a positive number See also Define configuration parameters for a SCARA Delta robot on page 105 Beginning with version 17 of the application you can use negative offsets for the X1b base offset on 2D and 3D delta geometries For example a mechanical 2D delta robot using a ...

Страница 106: ... the origin of the coordinate system X1 X2 intersection to P1 The Logix Designer application coordinate system configuration for the offset tab used with the preceding example is shown in the following example This negative offset description also applies for Delta 3D and SCARA Delta configurations The typical SCARA Independent robot has two revolute joints and a single prismatic joint This robot ...

Страница 107: ...09 The reference frame for the SCARA Independent geometry is at the base of link L1 The internal kinematic equations are written as if the start position for the SCARA Independent robot joints are as shown in this diagram J1 is measured counterclockwise around X3 axis starting at an angle of J1 0 0 when L1 is along the X1 axis J2 is measured counterclockwise starting with J2 0 when Link L2 is alig...

Страница 108: ...xis is configured as a member of both the source and target coordinate systems For additional information about establishing a reference frame see Articulated Independent robot Source coordinate system configuration Target coordinate system configuration See also Articulated Independent robot on page 65 The work envelope is the three dimensional region of space that defines the reaching boundaries...

Страница 109: ...e Link lengths The configuration parameter information is available from the robot manufacturer Tip Baseoffsetsand end effectoroffsets do notapply to aSCARA Independent robot The following example illustrates the typical configuration parameters for a SCARA Independent robot See also Link Lengths for SCARA Independent robot on page 110 Link lengths are the rigid mechanical bodies attached at joint...

Страница 110: ...sh the reference frame for a Cartesian Gantry robot on page 111 Identify the work envelope for a Cartesian Gantry robot on page 111 Define configuration parameters for a Cartesian Gantry robot on page 111 For a Cartesian Gantry robot the reference frame is an orthogonal set of X1 X2 and X3 axes positioned anywhere on the Cartesian robot All global coordinate measurements points are relative to thi...

Страница 111: ... the Local coordinate system and the reference frame For more information about Motion Instructions see Logix 5000 Controllers Motion Instructions Reference Manual publication MOTION RM002 The work envelope for a Cartesian Gantry robot is typically a solid rectangle of length width and height that is equal to the axis travel limits Defining the link lengths base offset or end effector offset confi...

Страница 112: ...r example when Motor A X1 axis is rotated the robot moves along a straight line at 45 angle Motor B X2 axis is rotated the machine moves at an angle of 45 Motors A and B are rotated clockwise at the same speed then the machine moves along a horizontal line Motors A and B are rotated counterclockwise at the same speed then the machine moves along a vertical line Any X Y position can be reached by p...

Страница 113: ... 5 moves to a real mechanical position of X1 10 X2 5 See also Establish the reference frame for a Cartesian H bot robot on page 113 Identify the work envelope for a Cartesian H bot robot on page 113 Define configuration parameters for a Cartesian H bot robot on page 113 For a Cartesian H bot the Base coordinate system is an orthogonal set of X1 X2 axes postponed anywhere on the Cartesian H bot The...

Страница 114: ......

Страница 115: ...ientation behavior The Coordinate Definition parameter in the Coordinate System Properties dialog box determines whether or not there is orientation support in the coordinate system See also Configure a Cartesian Coordinate System on page 39 This information provides information about the Cartesian coordinate frame A Cartesian coordinate frame is a set of orthogonal lines that intersect at an orig...

Страница 116: ...Translation describes the vector connecting two Cartesian points Orientation the three ordered rotations around the X Y and Z Cartesian axes Translation Specification Typically a point in space is specified by the three coordinates of the point with respect to the base coordinate system as shown in the following figure The three coordinates of the point are X Y Z This specification is also called ...

Страница 117: ...present a point in space and describe the orientation of a body in space See the orientation of the aircraft in the following diagram Orientation specifies the roll pitch and yaw orientation of a flying aircraft Roll pitch and yaw are standard navigation terms for airplanes and ships and represent the rotations around X Y and Z axes of the base coordinate system ...

Страница 118: ...position and orientation explained above describe the point in space with respect to the base frame as shown in the preceding diagram See also Transform Representation of Point on page 118 Orientation Specification on page 123 Point Conversion on page 125 RxRyRz flip mirror flip condition on page 126 Translation and Rotation example on page 132 The mathematical forms described above to specify the...

Страница 119: ...int specified by three vectors as shown in the figure above The approach vector a specifies how the object is approached by the robot s end effector as shown in the figure above The orientation vector o specifies orientation of the end effector fingertip to fingertip when approaching the object as shown in the figure above The final vector known as the normal vector n is a vector normal to the pla...

Страница 120: ...vectors with respect to the base coordinate system The columns of the rotation matrix n o a represent the direction cosines of the rotated orientation frame with respect to the base coordinate system Translation Specification of Point n o a t The translation and rotation specifications are combined to form a 4 by 4 transform matrix with elements from translation and orientation specification as sh...

Страница 121: ...esent transform that can be used to transform any point in the reference coordinate system to the target coordinate system And so the transform T to transform points from reference frame A to target frame B is given by the following matrix equation The transformation can be used to convert a point with respect to reference frame A to reference frame B using the following matrix equation ...

Страница 122: ...orked using matrix multiplication mathematics Rotation Transform Matrix R known as Rotation matrix transforms a base coordinate frame to the rotated coordinate frame as shown by the rotation around Y axis in the figure below The three rotation matrices which rotate base frame about the three base coordinate systems are important and rotate the base frame by angle Rx around X angle Ry around Y or a...

Страница 123: ... to handle for user defined points but as shown in the calculations above easy to map points from one coordinate frame to another coordinate frame E g End of Arm Frame to TCP frame When the points need to be taught it becomes difficult to teach approach and orientation vector to specify the orientation A representation that requires only three numbers to completely specify the orientation is more ...

Страница 124: ...e Logixfirmware usesthis conventionforspecifying the points Any point inCartesianspace is specified by6 numbers XYZRxRyRzwhereRx Ry and Rzare specifiedwithfixed angleconvention Start with a frame coincident with reference frame A First rotate B about Xa by an angle γ then rotate about Ya by an angle β and then rotate about Za by an angle α It is also important to note that order of rotation is imp...

Страница 125: ...Z infixedframe conventionisequivalent toZY X movingframe convention The two conventions described above are commonly used conventions There are other conventions like Z Y Z that user may be more familiar In all there are 12 fixed angle and 12 moving frame conventions It is possible to develop application code to convert from any of these conventions to fixed angle convention used by Logix embedded...

Страница 126: ...th Ry rotation of 90 that has multiple solutions This condition is described as gimbal lock condition which occurs at Ry equal to 90 The system has to handle this condition by picking a solution out of the multiple possible solutions Also solutions are not available when Ry rotates beyond 90 A rotation matrix can be used to rotate Rx Ry or Rz to any value in the range of 180 and obtain the rotatio...

Страница 127: ...360 around Y axis At the 90 point of Ry the Rx and Rz need to mirror flip as shown in the trends The following is a 3D diagram of a series of points with Ry which has four regions as shown in the diagram This covers 360 range of rotation around Y axis while restricting Ry to 90 using mirror flip implementation Rz rotation in XY plane flips from 45 to 135 ...

Страница 128: ...Chapter 4 Geometrieswithorientationsupport 128 Rockwell AutomationPublicationMOTION UM002F EN P February2018 Tip FornonflipangleRy ismeasuredwithZ axis and forflip conditionangleRy is measuredwithZ axis ...

Страница 129: ...P February2018 129 The trends above show the same Ry range in non flip and flip region and Rx 180 to 0 and Rz 45 t0 135 transitions at flip points Ry range goes from 90 to 0 flip negative to 90 to 90 non flip to 90 to 0 flip positive in this example Ry only has a range of 90 with flip points ...

Страница 130: ...orientationsupport 130 Rockwell AutomationPublicationMOTION UM002F EN P February2018 Important Eventhoughthe trendsforRx Ry andRzmaylookdiscontinuous the transformationsgenerate smooth trends forcorresponding J4 J5 and J6 axes ...

Страница 131: ...3D space with fixed angle rotations 0 0 0 180 70 45 and mirror image 0 0 0 0 70 135 The points are the same from orientation point of view at final orientation point but the orientation is achieved by rotating with different sequence The solid arrows show the fixed frame Dotted arrows show the orientation frames after each fixed angle rotation ...

Страница 132: ...0 In this example the Rz moves through multiple turns and has Rz flip points in addition to mirror flip points The Rx Ry Rz Mirror Image Point same trend shown from trends in Logix Designer Rx trend in red Ry in green and Rz in blue The point 0 88 84 is mirror flip condition In this example the Rz moves through multiple turns and has Rz flip points in addition to mirror flip points The following i...

Страница 133: ... of the translation matrix used with the translation vector of 5 0 3 T and rotation matrix of 45 around Y axis The transform matrix A TB is The translation matrix above can also be represented in user format with X 5 Y 0 Z 3 Rx 0 Ry 0 Rz 45 The point A P is with respect to base coordinate frame A with the translation vector of 4 0 5 T and rotation matrix of 0 rotation or identity matrix The point ...

Страница 134: ...he right translation and orientation or pose in the specified frame For further information on the methods to determine the point specifications in the example see the work frame and tool frame topics See also Work Frame example on page 139 Tool frame offsets on page 142 Cartesian Point Specification on page 116 Point Conversion on page 125 RxRyRz flip mirror flip condition on page 126 Studio 5000...

Страница 135: ...red with respect to a different coordinate frame other than the base coordinate frame of the robot such as conveyor vision camera system and pallets Define this new reference frame using the work frame offsets All target positions are measured from the work frames Tool Frame Associated with tools attached at the end of arm of a robot Define this new tool frame using the tool frame offsets The tool...

Страница 136: ...e diagram the relationship between different frames are shown using arrow pointing from one origin to another origin of the frame The arrow direction indicates which way the frames are defined The end of arm frame and work frame are defined from the base frame of the robot The Tool frame is defined from the end of arm frame All target positions are measured from the work frame using target frames ...

Страница 137: ... base frame as the default work frame Work frame ID helps define multiple work frames using the same tag variable with different ID numbers Set the ID member to a value greater than or equal to zero The following image shows the work frame offset configuration in the MCTO instruction and offset values defined for a work frame tag WorkFrame_Offset Status Attributes ActiveWorkFrameID and ActiveWorkF...

Страница 138: ... for different robot geometries supported by Logix Designer application Geometry Type Coordinate Definition Work Frame Offsets X Y Z Rx Ry RZ Delta J1J2J6 Allowed Allowed Allowed Not Allowed Not Allowed Allowed J1J2J3J6 Allowed Allowed Allowed Not Allowed Not Allowed Allowed J1J2J3J4J5 Allowed Allowed Allowed Not Allowed Not Allowed Allowed Tip Offset valuesmust be setto 0 forrestrictedorientation...

Страница 139: ... Y 50 Z 0 Rx 0 Ry 0 Rz 30 Positionfrom theWorkFrame P2 X 42 321 Y 33 301 Z 0 Rx 0 Ry 0 Rz 45 See also Define coordinate system frames on page 134 Work frame examples on page 139 Tool frame offsets on page 142 These examples illustrate how to use work frames in different scenarios Multiple work frames with one robot base frame Use work frames in scenarios where one robot works with multiple work fr...

Страница 140: ...d for the other pallets placed at different positions and orientations Use the MCTO instruction with different work frame offset values and run the same program The MCTO instruction re computes the new target positions based on the different work frame offset inputs For example the Position of Box 1 is same for all four pallets but the robot places at different positions and orientations from the ...

Страница 141: ...such as upside down and horizontal positions Work frame offsets set the relationship between the work frame and the base frames so that programing the target position is convenient for the users This diagram illustrates robots mounted in horizontal and upside down positions Work frame offsets 1 and 2 convert the target positions to conveyor coordinate system assuming it is placed on the ground Wor...

Страница 142: ...esents rotations around those axes Configure Offset parameters Configure the tool frame offsets in the MCTO or MCTPO instructions in Logix Designer application Measure the offset distance and rotation for the tool frame with respect to the robot s EOA frame axes Enter the degree of rotation offsets into the Rx Ry and Rz tag members in units of degrees Then enter the offset distances into the X Y a...

Страница 143: ...ctions as shown in this image ToolChangeAllowedStatus ToolChangeAllowedStatus attribute allows the user to change the tool dynamically through the MCTO instruction while coordinated moves are finished or any source axis is in motion through the MAG or MAPC instruction as a slave axis The ToolChangeAllowed bit is present in all coordinate systems and it is set in the source and target coordinate sy...

Страница 144: ...structiongenerates error 148forinvalidorientationoffsets Establish a Tool frame This diagram illustrates establishing a new Tool frame X Y Z from the EOA frame XYZ and change in the end position P of the robot with reference to a new Tool Frame The simple gripper tool is attached at the end plate of 4 axis delta robot TCP point is measured from the EOA frame of the End plate The Tool Frame X Y Z i...

Страница 145: ...ames on page 134 Tool frame example on page 145 Work frame examples on page 139 Work frame offsets on page 137 This illustration shows an example of using the Tool Frame in Pick Place applications The custom tooling with three grippers 1 2 and 3 is attached at the end of 4 axis Delta robot Each gripper is picking an object 1 2 3 6 placed at different orientations from the moving conveyor and then ...

Страница 146: ...e offsets The robot picks another object using second gripper Tip Referto ToolChangeAllowedStatusstatus bit fordynamically changing thetool frame offsets Ifthis bitis not set and newMCTO isinitiatedfortool changethennewMCTO will generate 61withextended error 10 Firstthe MCTOinstructionbit IP is clearedwhenthe second MCTO isinitiatedsuccessfully Tool Frames Tool ID Tool Frame Offsets X Y Z Rx Ry Rz...

Страница 147: ...oint 1 J1 Joint 2 J2 and Joint 6 J6 axes in the robot s coordinate system The three joint axes are either Directly programmed in joint space Automatically controlled by the kinematics calculations when instructions are executed in the application programmed in a virtual Cartesian coordinate system This robot contains a fixed top plate Base Plate and a moving bottom plate End Plate The fixed top pl...

Страница 148: ...rent work frame other than the default is defined program the Tool Center Point TCP to a full six axis Cartesian point X Y Z Rx Ry Rz The application computes the joint values J1 J2 J6 to move the TCP linearly from the current position to the programmed full Cartesian position using the programmed vector dynamics Since there is no rotation on Rx and Ry Orientation axis Rx orientation value can onl...

Страница 149: ...k of one of the arm is aligned along the positive X axis and the other to negative X axis Based on the right hand rule Z axis positive is the axis pointing up out of the paper in the top view as shown in the illustration J1 rotation is measured clockwise around the Y axis at the Base frame Y axis is pointing inside Direction of Joint Axis J1 and J2 in positive direction causes movement of the top ...

Страница 150: ...r Joints to move the robot 3 On the Scaling tab in the Axis Properties dialog box in the Transmission Ration I O box set the gear ratio for each axis 4 In the Scaling box enter the scaling to apply to each axis J1 J2 such that one revolution around the Link1 load rev equals 360 The same applies to the J6 axis One revolution of the J6 axis equals 360 5 Move all joints to the calibration position by...

Страница 151: ...each and payload capacities The configuration parameter values for the robot include Link lengths Base offsets Effector Plate offsets Swing Arm offsets Zero Orientation The configuration parameter information is available from the robot manufacturer Important Verify thatthe values fortheLink Lengths Base Offsets and End Effector Offsetsare entered inthe Coordinate System Properties dialogboxusing ...

Страница 152: ...page 152 Swing Arm Offsets for Delta J1J2J6 robot on page 153 Configure Zero Angle Orientation for Delta J1J2J6 robot on page 155 In a 3 axis Delta robot configuration Base and End plate offsets are represented as Rb and Re offsets Rb This offset represents the Base plate offset value Enter the value equal to the distance from the origin of the robot coordinate system to one of the actuator joints...

Страница 153: ...n parameters for Delta J1J2J6 robot on page 151 Swing Arm Offsets for Delta J1J2J6 robot on page 153 Configure Zero Angle Orientation Delta J1J2J6 robot on page 155 Configuring offset variables in a GSV SSV instruction on page 154 Use the Offsets tab in the Coordinate System Properties dialog box to enter the D3 Swing Arm Offsets value The D3 value is the distance on Z axis from the center of end ...

Страница 154: ... be zero based on the mechanical setup See also Configuration parameters for Delta J1J2J6 robot on page 151 Configure Zero Angle Orientations for Delta J1J2J6 robot on page 155 Configuring offset variables in a GSV SSV instruction on page 154 The Offset parameters in the Coordinate System Properties dialog box for the 3 axis Delta robot are not mapped to the attributes of the same name in the GSV ...

Страница 155: ...ion Joint 6 axis of rotation is aligned with Z axis of base frame when J6 is at 0 End of Arm EOA frame has Rx value of 180 with respect to base frame that results in Z axis pointing downward To have joints J1 and J2 angular positions to be any value other than 0 when L1 is horizontal then configure the Zero Angle Orientation values on the Geometry tab in the Coordinate System Properties dialog box...

Страница 156: ...a robot geometries the internal transformation equations in the Logix Designer application assume Joints J1 J2 are at 0 when link L1 is horizontal parallel to XY The work envelope is the two dimensional region of space that defines the reaching boundaries for the robot arm using the default work and tool frame settings The typical work envelope for a Delta robot looks similar to a two dimensional ...

Страница 157: ...lculated based upon the Link Lengths and Offset values entered on the Geometry and Offsets tabs of the Coordinate System Properties dialog box For more information about the maximum positive and maximum negative joint limits refer to Maximum Joint Limit Conditions Work and Tool Frame Offset Limits During each scan the joint positions are checked to ensure that they are within the maximum and minim...

Страница 158: ...2 Positive joint limit condition The derivations for the maximum positive joint apply to the condition when L1 and L2 are collinear Maximum Positive Joint Limit Position R absolutevalueof Rb Re Maximum J1 J2 Negative joint limit condition The derivations for the maximum negative joint limit apply to the condition when L1 and L2 are folded back on top of each other R is computed by using the base a...

Страница 159: ...2018 159 MaximumNegative JointLimit Condition R absolutevalueof Rb Re Maximum J6 joint limit condition The J6 axis is the rotational axis that could have multiple turns The maximum number of turns supported is 127 Maximum positive and negative range is checked based on number of turns supported on J6 ...

Страница 160: ... can reach only up to limited orientation positions Work and Tool frame offset values are limited up to reachable work envelope The following offset values are allowed for Work and Tool frames The MCTO instruction generates error 148 for invalid offset values Offset values on X Y Z and Rz axis are allowed for the Work Frame offsets Rx and Ry offsets are restricted and must be set to 0 Specify thes...

Страница 161: ...moves in six dimensional Cartesian X Y Z Rx Ry Rz space is often called a spider or umbrella robot This illustration is an example of a four dimensional Delta robot In Logix Designer application the four degrees of freedom are configured as four joint axes J1 J2 J3 and J6 in the robots coordinate system All joint axes are either Directly programmed in joint space Automatically controlled by the em...

Страница 162: ...MCTO instruction computes the joint values J1 J2 J3 and J6 to move the TCP linearly from the current position to the programmed full Cartesian position using the programmed vector dynamics In four axis Delta robots the End Plate always remains parallel to Base plate in XY Plane As a result program the Rx Ry and Rz orientation values with following valid range of values OrientationAxis Valid Ranges...

Страница 163: ...long the X positive axis as shown in the Top View figure The Side View figure shows that the X axis will pass through the center of J1 s motor to the center of Link L1 and L2 joint Moving in the counter clockwise direction from J1 to J2 and J3 the Y axis is orthogonal to the X axis Based on the right hand rule Z positive axis is the axis pointing up in side view out of the paper in the top view J1...

Страница 164: ...164 Use these steps to calibrate a Delta J1J2J3J6 robot To calibrate a Delta J1J2J3J6 robot 1 Obtain the angle values from the robot manufacturer for J1 J2 J3 and J6 at the calibration position Use these values to establish the reference position 2 Refer to manufacturer s datasheet to determine if the associated sized motor contains an internal or external gearbox from the motor to actuation at th...

Страница 165: ...e L1 is in a horizontal position XY Plane 8 If the top link of arm L1 is not in a horizontal position configure the values for the Zero Angle Offsets on the Geometry tab in the Coordinate System Properties dialog box to be equal to the values of the joints when in a horizontal position 9 Move J6 to an absolute position of 0 0 Verify that joint position reads 0 and the J6 position is in the Z axis ...

Страница 166: ...ffector Plate dimensions for Delta J1J2J3J6 robot on page 167 Swing Arm offsets for Delta J1J2J3J6 robot on page 168 Configure Zero Angle Orientation for Delta J1J2J3J6 robot on page 170 Link lengths are the rigid mechanical bodies attached at the rotational joints The four dimensional Delta robot geometry has three link pairs made up of L1 and L2 Each link pair has the same dimensions L1 link att...

Страница 167: ...elta J1J2J3J6 robot on page 170 In a 4 axis Delta robot configuration Base and End plate offsets are represented as Rb and Re offsets Rb This offset represents the Base plate offset value Enter the value equal to the distance from the origin of the robot coordinate system to one of the actuator joints Re This offset represents the End plate offset value Enter the value equal to the distance from t...

Страница 168: ...guration parameters for Delta J1J2J3J6 robot on page 165 Swing Arm offsets for Delta J1J2J3J6 robot on page 168 Configuring offset variables in a GSV SSV instruction on page 169 Configure Zero Angle Orientations for Delta J1J2J3J6 robot on page 170 In the 4 axis Delta robot configuration only one Swing Arm Offset D3 is allowed The D3 value is the distance on Z axis from the center of end plate to ...

Страница 169: ...m Offset values for the project Enter the Swing Arm Offset values on the Offsets tab in the Coordinate System Properties dialog box See also Configuration parameters for Delta J1J2J3J6 robot on page 165 Configurable variable to attribute name mapping on page 169 Configure Zero Angle Orientation for Delta J1J2J3J6 robot on page 170 The Offset parameters in the Coordinate System Properties dialog bo...

Страница 170: ...rresponding joint axis J1 J2 or J3 is rotating in the positive direction Joint 6 axis of rotation is aligned with Z axis of the base frame When J6 is at 0 End of Arm EOA frame is rotated by 180 on Rx Z axis pointing down with respect to base frame To have joints J1 J2 and J3 angular positions to be any value other than 0 when L1 is horizontal then configure the Zero Angle Orientation values on the...

Страница 171: ...M002F EN P February2018 171 Example of Zero Angle Orientation set up in 4 axis Delta robot See also Configuration parameters for Delta J1J2J3J6 robot on page 165 Link Lengths for Delta J1J2J3J6 robot on page 166 Base and Effector Plate dimensions for Delta J1J2J3J6 robot on page 167 ...

Страница 172: ...he Delta robot geometries When an MCTO instruction is invoked for the first time the maximum positive and maximum negative joint limits are internally calculated based upon the Link Lengths and Offset values entered on the Geometry and Offsets tabs of the Coordinate System Properties dialog box For more information about the maximum positive and maximum negative joint limits refer to Maximum Joint...

Страница 173: ...e condition when L1 and L2 are collinear Maximum Positive Joint Limit Position R absolute value of Rb Re Maximum J1 J2 J3 negative joint limit condition The derivations for the maximum negative joint limit apply to the condition when L1 and L2 are folded back on top of each other R is computed by using the base and end effector offsets values Rb and Re MaximumNegative JointLimit Condition R absolu...

Страница 174: ...es defined in the MCTO and MCTPO instruction The target end position range changes based on the Work and Tool Frame offsets In the Delta robot the End plate is always parallel to the Base plate and the 4 axis Delta robot can reach only up to limited orientation positions Work and Tool frame offset values are limited up to reachable work envelope The following offset values are allowed for Work and...

Страница 175: ...ublic Public Documents Studio 5000 Sample ENU v current_release Rockwell Automation This illustration shows a five axis Delta robot that moves in six dimensional Cartesian X Y Z Rx Ry Rz space It is often called a spider or umbrella robot In the Logix Designer application the five degrees of freedom are configured as five joint axes J1 J2 J3 J4 J5 in the robots coordinate system The five joint axe...

Страница 176: ...e J4 axis it rotates and tilts the swing arm due to internal gearing To compensate this tilt effect the robot needs to move the J5 axis This relationship is set using J4 J5 Coupling Ratio and Coupling Direction on the Offsets tab in the Coordinate System Properties dialog box Program the Tool Center Point TCP to a X Y Z Rx Ry Rz coordinate Then the application computes the commands necessary for e...

Страница 177: ...nate system in the Logix Designer application with the joints homed as 0 in the XY plane then L1 of one of the link pairs is aligned along the X positive axis as shown in top view The side view shows the X axis passing through the center of Joint 1 s motor to the center of Link L1 and L2 joint Moving in the counter clockwise direction from Joint 1 to Joint 2 and Joint 3 the Y axis is orthogonal to...

Страница 178: ... set with reference to J4 position When J4 axis is homed to 0 position J5 rotation is aligned with the Y axis of Base frame At J5 home position swing arm link D5 should be vertical aligned with X axis of Base frame The following illustration show axis of rotations and their directions for J4 and J5 Tip Incase of couplingto preventtiltmotioncausedby J4homing first homethe J4 to 0 thenhome J5 to0 wi...

Страница 179: ...joints to the calibration position by jogging the robot under programmed control or manually moving the robot when the joint axes are in an open loop state 6 Do one of the following a Use the Motion Redefine Position MRP instruction to set the positions of the joint axes to the calibration values obtained in step 1 b Set the configuration value for the joint axes home position to the calibration v...

Страница 180: ...ot manufacturer Important Verify thatthe values fortheLink Lengths Base Offsets and End Effector Offsetsare entered inthe Coordinate System Properties dialogboxusing the samemeasurement units See also Link Lengths for Delta J1J2J3J4J5 robot on page 180 Base and Effector Plate dimensions for Delta J1J2J3J4J5 robot on page 181 Swing Arm Offsets for Delta J1J2J3J4J5 robot on page 182 Coupling between...

Страница 181: ...J5 robot on page 181 Swing Arm Offsets for Delta J1J2J3J4J5 robot on page 182 Coupling between J4 and J5 axis on page 186 Configure Zero Angle Orientations for Delta J1J2J3J4J5 robot on page 188 In a 5 axis Delta robot configuration Base and End plate offsets are represented as Rb and Re offsets Rb This offset represents the Base plate offset value Enter the value equal to the distance from the or...

Страница 182: ... enter the base offset and effector plate offset for the 5 axis Delta robot See also Configuration parameters for Delta J1J2J3J4J5 robot on page 180 Swing Arms offsets for Delta J1J2J3J4J5 robot on page 182 In the 5 axis Delta robot configuration the Joint 4 and Joint 5 axis are configured using Swing Arm offsets A3 D3 A4 D4 and D5 Denavit Hartenberg DH notation is used to configure these offset v...

Страница 183: ... X axis from center of end plate to the J4 axis of rotation D4 The distance on Z axis from the J4 axis of rotation to the J5 axis of rotation A4 The distance on X axis from the J4 axis of rotation to the J5 axis of rotation D5 The distance on Z axis from the J5 axis of rotation to the EOA frame Tip Forall SwingArmoffsets positive Zdirectionis pointing downatthe End plate centerpoint Refer to the m...

Страница 184: ...center point The table shows configuring offsets and Swing Arm Offset values Configuring offsets Swing Arm offset value Joint4 axis is starting rightatthe End plate centerpoint so A3 andD3 offsetsare zero D3 0 A3 0 Joint5 isat adistance from Joint4 Distanceonthe positive X axis is configuredas A4 30mm distanceonpositive Zaxis is measured asD4 50mm D4 50 A4 30 From Joint5to EOA ismeasuredasD5 75mm ...

Страница 185: ...ing Arm Offset values Configuring offsets Swing Arm offset value Joint4 axis isat adistance from End plate centerpoint Offset distance inXpositivedirectionis measured as A3 50mm andinZ positive directionisasmeasuredas D4 25mm Inthis setup D3 canalso beused inplace of D4 A3 50 D4 25 Joint4 and Joint5 areintersecting eachothersoD3 and A4offset values arezero D3 0 A4 0 From Joint5to EOA ismeasuredasD...

Страница 186: ...ot on page 180 Configure Zero Angle Orientations for Delta J1J2J3J4J5 robot on page 188 Some five dimensional Delta robots have a mechanical coupling between the J4 and J5 axis Rotation of the Swing Arm causes the tilt movement on D5 offset link To compensate for this tilt motion move the J5 axis in the same or opposite direction of the J4 axis move with relative gear ratio Coupling between J4 and...

Страница 187: ...The Coupling attributes applyonly to the Delta J1J2J3J4J5robot Coupling Direction This parameter indicates the direction of the coupling between J4 and J5 There are 3 options to choose from none No coupling relation between J4 and J5 Same Coupling between J4 and J5 is in same direction that is J4 positive rotation causes the tilt motion in the same direction of the positive J5 motion Opposite Coup...

Страница 188: ...geometries the internal transformation equations in the Logix Designer application assume Joints J1 J2 and J3 are at 0 when link L1 is horizontal in the XY plane As each top link L1 moves downward its corresponding joint axis J1 J2 or J3 is rotating in the positive direction Joint 4 axis of rotation is aligned with Z axis and Joint 5 axis or rotation is aligned with Y axis of the base frame When J...

Страница 189: ... link is at horizontal position shown in the image below then enter 90 in the Z5 parameter for Joint 5 The Z4 offset can be used to set Joint 4 axis other than default 0 position Example of Zero Angle Orientation set up in 5 axis Delta robot See also Configuration parameters for Delta J1J2J3J4J5 robot on page 180 Link Lengths for Delta J1J2J3J4J5 robot on page 180 ...

Страница 190: ...CTO instruction internally calculates the joint limits for the Delta robot geometries When an MCTO instruction is invoked for the first time the maximum positive and maximum negative joint limits are internally calculated based upon the Link Lengths and Offset values entered on the Geometry and Offsets tabs of the Coordinate System Properties dialog box For more information about the maximum posit...

Страница 191: ...e condition when L1 and L2 are collinear Maximum Positive Joint Limit Position R absolute value of Rb Re Maximum J1 J2 J3 negative joint limit condition The derivations for the maximum negative joint limit apply to the condition when L1 and L2 are folded back on top of each other R is computed by using the base and end effector offsets values Rb and Re MaximumNegative JointLimit Condition R absolu...

Страница 192: ...s computed based on J4 axis limit J5 axis can move beyond this 179 range but the effective Swing Arm tilt motion is restricted between 179 For example if J4 J5 coupling ratio is 2 1 and J4 range is 720 then J5 can move up to 360 to compensate for coupling effect Configure the joint limits Refer to robot manufacturer s data sheet to compute the range of J1 J2 J3 J4 and J5 axes These limits are set ...

Страница 193: ...estricted and must be set to 0 Specify these offsets through the ToolFrame parameter in the MCTO instruction See also Identify the Work Envelope for Delta J1J2J3J4J5 robot on page 190 The following image is an example of a typical pick and place application with the Delta robot It illustrates how the 5 axis Delta robot picks up the boxes from the conveyor and places them on the table with differen...

Страница 194: ...n the Motion Coordinated Path Move MCPM instruction For example first box s XYZ position form the conveyor is 200 200 50 and it is rotated by 30 on Rz axis so P1 position is programmed as 200 200 50 180 0 30 in MCPM instruction During point P2 to P3 move Rz value at TCP changes from 30 to 90 and Ry value changes from 0 to 90 Boxes are placed on a table with different Rx Ry and Rz orientations For ...

Страница 195: ...oves of such systems are specified Tips Mirrorimage behavioroccurs onlywhenMotionCoordinated TransformwithOrientation MCTO transformsare active The mirrorimagepositiondata assumes no Tool orWorkframeorientationoffsets areapplied Ry orientationonthe Delta J1J2J3J4J5 has oppositesignof J5 joint position See Configuring the Delta J1J2J3J4J5 CoordinateSystem formore details Important Avoidusing the Mo...

Страница 196: ...ar in behavior to the Rz J4 transform position relationship When the J5 axis crosses the ninety degree boundary the Ry axis position no longer tracks the inverse of J5 Instead the Ry position reflects a positive correlation with J5 This range of operation is referred to as mirror flip region See also Rx axis position in mirror non flip and flip regions on page 196 Rz axis position in mirror non fl...

Страница 197: ...irror image Ry orientation on page 196 Robot geometries that exhibit the mirror image Ry position behavior have an impact on the Rz position depending on which region the Ry axis is operating This relationship is shown in the following table Region J4 range Rzposition mirrornon flip 180 J4 180 J4 mirrorflip 0 J4 180 J4 180 0 mirrorflip 180 J4 0 J4 180 0 Tip The Rzflip inpositiondoes not result ina...

Страница 198: ...elease Rockwell Automation The following orientation angle specifications are not allowed in Logix Designer application due to singularity conditions involving multiple solutions or other scenarios involving Euler angle specification The orientation Rx 180 0 Ry 90 0 is mathematically correct but is not allowed in Logix Designer application due to ambiguity with the Rx 0 0 Ry 90 0 specification Alw...

Страница 199: ...to demonstrate the mirror image effect on Rx and Rz without generating actual changes in orientation in those dimensions Example Start Region End Region Notes 1 Mirrorflip Mirrornon flip Starting orientation Rx 0 Ry 78 Rz 180 withMotionCoordinated PathMove MCPM movetoorientation Rx 180 Ry 45 Rz 0 The resultantmove is 57 onRy 57 onJ5 andRxflips from 0 to 180 andRz flips from 180 to0 when Ry crosses...

Страница 200: ...inate fromtheabsoluteorientationspecified Tip Anincremental Rymoveof distance180 is allowed here thedirectionof themoveis explicitly specified by the signofthe distance parameter 6 Mirrorflip Mirrorflip Shortest rotary pathmove forRyis not allowed inthe Mirrorflip region Example4 shows howsucha moveis planned Tip Incrementalmovesare not limited like absolutemoves are However suchincremental Rymove...

Страница 201: ... system and four joint axes which form the non Cartesian coordinate system Cartesian and joint target points for Delta J1J2J3J6 robot system A point in space may be described in two different ways as a set of Cartesian coordinates Euclidean space and as a set of robot joint angles joint space Since there is no rotation on Rx and Ry Orientation axis only program the Rx orientation value to 180 The ...

Страница 202: ...Rz is counterclockwise around the Z axis of the robot base frame However the positive rotation for J6 axis is clockwise around the Z axis of the robot base frame which is opposite to Rz axis rotation With the 3D Delta robot system since there is no rotation possible around X and Y axis of base frame the only rotation possible is around Z axis As a result the Cartesian coordinate system can be desc...

Страница 203: ...ctual max number of turns is geometry dependent The 3 Turns Counters are elements of a single array attribute of the target coordinate system which contain J1 J4 or J6 axes turns counters Tips IfRz reaches thepoint 180 but doesnotcross it it does notflip and staysat180 IfRz reaches the point 180 it flips to 180 If eithertheworkframeorthe toolframeoffset onRzis not 0 turns counters still incrementw...

Страница 204: ...nter and J6 values that are shown in the trends in figures above Rz Turns Counter of J6 J6 if zeroangle offset 0 and Rzwork Offset 0 J6 if zeroangle offset 0 and Rzwork offset 80 J6 if zeroangle offset 90 and work Offset 0 179 9999 2 540 0001 460 0001 630 0001 180 2 540 460 630 179 9999 1 539 9999 459 9999 629 9999 0 1 360 280 450 ...

Страница 205: ...e systems Refer to configuring Cartesian and robot coordinate systems for details of configuring the two coordinate systems that are used for the turns counter application example The example uses the Delta J1J2J3J4J5 robot system In this example the source Cartesian coordinate system has six virtual axes X Y Z Rx Ry Rz The robot coordinate system has five real axes J1 J2 J3 J4 J5 The example uses...

Страница 206: ...uction Align Cartesian and Robot Coordinate systems The following ladder logic illustrates moving the robot coordinate system to an initial position before enabling the transformation The transformation sets up the robot to a known position Set up Master Driven instructions for Cartesian dynamics control This ladder logic illustrates setting up the Master Driven Speed Control MDCC instruction and ...

Страница 207: ...inate system and target 5 axis Delta robot system Move the source side to the desired target positions using MCPM path data with turns counter specifications Refer to this ladder logic to command the robot to move to a target point in the Cartesian space specified by an element of an array of PATH_DATA points See MCPM programming instructions and sample programs for details on ladder logic to move...

Страница 208: ...on and orientation of any point defined has six coordinates XYZRxRyRz The translation coordinates are the coordinates of target point with respect to the base coordinate systems The orientation coordinates are fixed angle rotations first around X axis followed by second rotation around Y axis of the fixed robot base frame and third rotation around Z axis of the fixed robot base frame ...

Страница 209: ... axis for Delta J1J2J6 and Delta J1J2J3J6 robots For Delta J1J2J3J4J5 the turns counter is associated with Rz rotation and J4 axis The J6 or J4 axis rotates multiple revolutions around the Z axis shown in the previous diagram To fully specify the correct orientation the Rz orientation must specify the desired orientation with which turn of joint axis For example 45 with turns counter 0 and 45 with...

Страница 210: ...TOis enabled onthe Cartesiancoordinatesystem MCPM withnonzero turns counterwill errorif theMCTO isnotenabledonthe Cartesiancoordinate system For programming the multi turn axis such as J6 for Delta J1J2J3J6 specify the shortest or longest path for J6 axis by specifying the Rz position and turns counter See the following diagram for absolute moves ...

Страница 211: ...preadsheet for Delta J1J2J3J6 as absolute move with turns counter Program the MCPM target points in incremental mode MoveType 1 The incremental moves are programmed differently and are not restricted to 180 Program multiple turns using just positive or negative displacements more than one turn The system also enforces turns counters set to 0 in incremental move These PATH_DATA points show typical ...

Страница 212: ...bot can be moved to desired position using HMI panel and the turns counter data along with Cartesian data can be used to program the target point for the MCPM move Getting positions for PATH_DATA target points for MCPM instruction using MCTPO turns counter data Sometimes after powerup or shutdown only joint positions are known while continuing from the current position Use the MCTPO instruction to...

Страница 213: ... usethis Kinematicsample projects ontheHelpmenu clickVendor SampleProjects and thenclickthe Motion category The Rockwell Automationsample project s default locationis c Users Public Public Documents Studio5000 Sample ENU v current_release Rockwell Automation See also Configure and program turns counters on page 200 ...

Страница 214: ......

Страница 215: ...n Schedule on page 226 Camming is the process of coordinating the movement of two axes a master axis and a slave axis where the movement of one is completely dependent on the movement of the other There are two types of camming Mechanical camming Electronic camming See also Mechanical camming on page 215 Electronic camming on page 216 In mechanical camming the master axis functions as a cam A cam ...

Страница 216: ...ectronic camming Creates coordinated motion profiles that are functions of the time o relative position of another axis Allows you to configure higher cam velocities Is defined by using a point pair table of values This table is a master axis set of point positioning values and a corresponding set of slave axis point positioning values The user defined position point array causes one closed loop a...

Страница 217: ... Axis Position Cam MAPC instructions Upon execution of this instruction the slave axis is synchronized with the master axis See the Logix 5000 Controllers Motion Instructions Reference Manual publication MOTION RM002 for more information on how to configure the position cam profile in an MAPC instruction Linear and Cubic Interpolation The resultant calculated cam profiles are fully interpolated Th...

Страница 218: ...s not correspond exactly with a point in the cam table associated with the cam profile the slave axis position is determined by linear or cubic interpolation between the adjacent points In this way the smoothest possible slave motion is provided Each point in the cam array that was used to generate the time cam profile can be configured for linear or cubic interpolation Electronic camming remains ...

Страница 219: ...each required slave axis change of position as corresponds to specific master axis position or time positions See also Acceleration Cam Profile on page 219 Run Cam Profile on page 220 Deceleration Cam Profile on page 220 Dwell Cam Profile on page 221 An acceleration cam profile determines a slave axis acceleration to a particular position This graphic illustrates a sample acceleration cam profile ...

Страница 220: ...ion and remains steady until the end of the cam profile This graphic illustrates a sample run cam profile in the Logix Designer programming software Cam Editor See also Use Common Cam Profiles on page 219 A deceleration cam profile determines a slave axis deceleration from a particular position This graphic illustrates a sample deceleration cam profile in the Logix Designer programming software Ca...

Страница 221: ...mmon Cam Profiles on page 219 A dwell cam profile stops all slave axis movement until another cam profile begins operation Typically a dwell cam profile follows a deceleration cam profile This graphic illustrates a sample dwell cam profile in the Logix Designer programming software cam editor Dwell CamProfile ...

Страница 222: ...u need to execute the MAPC instructions in the right order For example if you want to run only one slave cycle start with the Accel_Profile and pend the Decel_Profile immediately that results in 2 x 1 2 Cycle 1 Cycle These are executed at the same point in time Set the execution schedule in the MAPC instruction for Acceleration as Immediate Set the Deceleration to Pending Behavior of Pending Cams ...

Страница 223: ...erate a family of specific cam profiles Scaling works slightly differently when it is used with an MAPC instruction that is in position cam profiles than when it is used with an MATC instruction that is in time cam profiles See also Scaling Position Cam Profile on page 223 Scaling Time Cam Profiles on page 224 A position cam profile can be scaled in both the master dimension and slave dimension wh...

Страница 224: ...approximately equal to those of the unscaled profile the Master Scaling and Slave Scaling values should be equal For example if the Slave Scaling value of a profile is 2 the Master Scaling value should also be 2 to maintain approximately equal velocities and accelerations during execution of the scaled position cam Important Decreasingthe MasterScaling value orincreasingtheSlaveScaling valueof a p...

Страница 225: ...be 2 This requirement is to maintain approximately equal velocities and accelerations during execution of the scaled time cam Important If you decreasethe TimeScaling valueorincreasethe Distance Scalingof atime cam it increases the required velocitiesand accelerationsofthe profile This actioncancausea motionfaultifthe capabilities of the drive system are exceeded See also Scaling Position Cam Prof...

Страница 226: ...motiononly resumeswhenthemastermoves backintothe profile range specified bythe startand end points 1 This section is only available on the MAPC instruction The Execution Schedule parameter controls the execution of an instruction Configure the Execution Schedule parameter on an MAPC or MATC instruction The Execution Schedule selections are different depending on which instruction that is the MAPC ...

Страница 227: ...according to the specified Cam Profile The fact that the Position Cam Lock Status bit for the specified slave axis is also set indicates this condition Changing the Cam Lock Position on an MAPC Immediate Execution Schedule The Cam Lock Position parameter of the MAPC instruction determines the starting location within the cam profile when the slave locks to the master Typically the Cam Lock Positio...

Страница 228: ...can use Execution Schedule selection of Pending to blend two position cam profiles together without stopping motion This Execution Schedule selection of Pending is fully described in Pending Cams topic Forward Only Reverse Only or Bidirectional Execution Schedules The slave axis is not locked to the master until the master axis satisfies the condition that is specified when the Execution Schedule ...

Страница 229: ...ponding slave axis position from the defined cam profile This condition is important for applications where the master axis is a rotary axis because the position cam is then unaffected by the position unwind process When the master axis moves out of the range that the cam profile defines if Execution Mode is Once the following occur It clears the Position Cam Lock Status It clears the Position Cam...

Страница 230: ... also set This process is shown in the following figure If the Execution Schedule parameter is set to Immediate the axis is immediately locked to the time master coordinate according to the specified Cam Profile If an MATC instruction is executed on an axis that is already actively time camming an Illegal Dynamic Change error is generated error code 23 The only exception for this occurrence is if ...

Страница 231: ...d into the operating cam profile which is typically executed continuously To stop the slave axis the operating cam profile is smoothly blended into a deceleration profile such that the axis stops at a known location as shown in this diagram MAPC Instruction MATC Instruction By executing the position cam profile as a Pending cam profile while the current profile is still executing the appropriate c...

Страница 232: ...relative to the first profile at the time of the change and uses this information to maintain synchronization between the profiles If the Execution Schedule of an instruction is set to Immediate and a position or time cam profile is in process the instruction errs In this case the instruction generates an Illegal Dynamic Change error error code 23 in the programming software This error even occurs...

Страница 233: ...artesian coordinatesystem configure 43 program with noorientation 46 program with orientation 49 Cartesian Gantry 115 configuration parameters 115 establish referenceframe 115 identify theworkenvelope 115 Cartesian H bot 116 configuration parameters 117 establish referenceframe 117 identify theworkenvelope 117 Cartesian point specification 120 Collinear Moves velocity profiles terminationtypes 59 ...

Страница 234: ...8 end effectoroffsets 99 link lengths 98 maximumnegative joint limitcondition 95 97 maximumpositivejoint limit condition 95 96 reference frame 93 work envelope 95 Delta two dimensional 100 base offsets 104 calibrate 102 configuration parameters 103 end effectoroffsets 105 establishthe referenceframe 101 link lengths 104 work envelope 102 Determinecoordinatesystemtype 38 E electronic camming 222 ex...

Страница 235: ...200 204 210 MotionCoordinated Stop MCS 59 MotionCoordinatedTransform MCT 46 O Orientation specification 127 P pending cams 237 pointconversion 129 position camprofile 222 program with noorientation 46 blendedmoveswith MCLM andMCCM 47 example ladder diagram 47 program with orientation 49 blending path moveswith MCPM 49 superimposedmotionwith MCPM 53 use MCPM blendingwithorientation 51 R RxRyRz flip...

Страница 236: ...ance If you experience a problem within the first 24 hours of installation review the information that is contained in this manual You can contact Customer Support for initial help in getting your product up and running United StatesorCanada 1 440 646 3434 OutsideUnitedStates orCanada Use theWorldwideLocatoravailableat http www rockwellautomation com locations orcontactyourlocal Rockwell Automatio...

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