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R01AN5644EJ0100  Rev.1.00 

 

Page  46  of 62 

Jan 22, 2021 

 

Reference Guide for a 2-Axis Robot Arm with 2-Phase Stepping 

Motors Incorporating Resolvers 

RX24T, RX72M, 

RAA3064002GFP/RAA3064003GFP 

Obtain the inverse-Jacobian matrix. 

� 𝐿𝐿

1

cos

𝜃𝜃

1𝑖𝑖−1

+

𝐿𝐿

2

cos(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

𝐿𝐿

2

cos(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

−𝐿𝐿

1

sin

𝜃𝜃

1𝑖𝑖−1

− 𝐿𝐿

2

sin(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

−𝐿𝐿

2

sin(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

�

−1

 

 
In the inverse-Jacobian matrix, replace the equations with the following contents. 

cos

𝜃𝜃

1𝑖𝑖−1

= cos 1

, 

cos(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

) = cos 1

𝑝𝑝

2

, 

sin

𝜃𝜃

1𝑖𝑖−1

= sin 1

, 

sin

𝜃𝜃

2𝑖𝑖−1

= sin 2

, 

sin(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

) = sin 1

𝑝𝑝

2

 

� 𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

𝐿𝐿

2

cos 1

𝑝𝑝

2

−𝐿𝐿

1

sin 1

− 𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

sin 1

𝑝𝑝

2

�

−1

 

=

1

(

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2) × (

−𝐿𝐿

2

sin 1

𝑝𝑝

2)

−

(

𝐿𝐿

2

cos 1

𝑝𝑝

2) × (

−𝐿𝐿

1

sin 1

− 𝐿𝐿

2

sin 1

𝑝𝑝

2)

�

−𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

cos 1

𝑝𝑝

2

−

(

−𝐿𝐿

1

sin 1

− 𝐿𝐿

2

sin 1

𝑝𝑝

2)

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

�

 

=

1

(

−𝐿𝐿

1

𝐿𝐿

2

cos 1 sin 1

𝑝𝑝

2) +

�−𝐿𝐿

2

2

cos 1

𝑝𝑝

2 sin 1

𝑝𝑝

2

�

+ (

𝐿𝐿

2

𝐿𝐿

1

sin 1 cos 1

𝑝𝑝

2) +

�𝐿𝐿

2

2

cos 1

𝑝𝑝

2 sin 1

𝑝𝑝

2

�

�

−𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

cos 1

𝑝𝑝

2

𝐿𝐿

1

sin 1 +

𝐿𝐿

2

sin 1

𝑝𝑝

2

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

�

 

=

1

(

−𝐿𝐿

1

𝐿𝐿

2

cos 1 sin 1

𝑝𝑝

2) + (

𝐿𝐿

2

𝐿𝐿

1

sin 1 cos 1

𝑝𝑝

2)

�

−𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

cos 1

𝑝𝑝

2

𝐿𝐿

1

sin 1 +

𝐿𝐿

2

sin 1

𝑝𝑝

2

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

�

 

=

1

𝐿𝐿

1

𝐿𝐿

2

(sin 1 cos 1

𝑝𝑝

2

−

cos 1 sin 1

𝑝𝑝

2)

�

−𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

cos 1

𝑝𝑝

2

𝐿𝐿

1

sin 1 +

𝐿𝐿

2

sin 1

𝑝𝑝

2

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

�

 

From the additive theorem of trigonometric functions: 

=

1

−

𝐿𝐿

1

𝐿𝐿

2

𝑠𝑠𝐸𝐸𝐸𝐸

  2

�

−𝐿𝐿

2

sin 1

𝑝𝑝

2

−𝐿𝐿

2

cos 1

𝑝𝑝

2

𝐿𝐿

1

sin 1 +

𝐿𝐿

2

sin 1

𝑝𝑝

2

𝐿𝐿

1

cos 1 +

𝐿𝐿

2

cos 1

𝑝𝑝

2

�

 

 
Replace part of the equation for obtaining the current joint angle with the above. 

�𝜃𝜃

1𝑖𝑖

𝜃𝜃

2𝑖𝑖

�

=

�𝜃𝜃

1𝑖𝑖−1

𝜃𝜃

2𝑖𝑖−1

�

+

1

−𝐿𝐿

1

𝐿𝐿

2

sin

𝜃𝜃

2𝑖𝑖−1

�

−𝐿𝐿

2

𝑠𝑠𝐸𝐸𝐸𝐸

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

−𝐿𝐿

2

𝑦𝑦𝐸𝐸𝑠𝑠

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

𝐿𝐿

1

𝑠𝑠𝐸𝐸𝐸𝐸 𝜃𝜃

1𝑖𝑖−1

+

𝐿𝐿

2

𝑠𝑠𝐸𝐸𝐸𝐸

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

𝐿𝐿

1

𝑦𝑦𝐸𝐸𝑠𝑠 𝜃𝜃

1𝑖𝑖−1

+

𝐿𝐿

2

𝑦𝑦𝐸𝐸𝑠𝑠

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)

� �

𝑑𝑑𝑋𝑋

𝑖𝑖

𝑑𝑑𝑡𝑡

𝑑𝑑𝑌𝑌

𝑖𝑖

𝑑𝑑𝑡𝑡

�

 

 
Solve the determinant. The following equations are actually included in the program. 

𝜃𝜃

1𝑖𝑖

=

𝜃𝜃

1𝑖𝑖−1

+

1

−𝐿𝐿

1

𝐿𝐿

2

sin

𝜃𝜃

2𝑖𝑖−1

�−𝐿𝐿

2

𝑠𝑠𝐸𝐸𝐸𝐸

(

𝜃𝜃

1𝑖𝑖

+

𝜃𝜃

2𝑖𝑖

) ×

𝑑𝑑𝑋𝑋

𝑖𝑖

𝑑𝑑𝑡𝑡 − 𝐿𝐿

2

𝑦𝑦𝐸𝐸𝑠𝑠

(

𝜃𝜃

1𝑖𝑖

+

𝜃𝜃

2𝑖𝑖

) ×

𝑑𝑑𝑌𝑌

𝑖𝑖

𝑑𝑑𝑡𝑡 �

 

𝜃𝜃

2𝑖𝑖

=

𝜃𝜃

2𝑖𝑖−1

+

1

−𝐿𝐿

1

𝐿𝐿

2

sin

𝜃𝜃

2𝑖𝑖−1

�

{

𝐿𝐿

1

𝑠𝑠𝐸𝐸𝐸𝐸 𝜃𝜃

1𝑖𝑖−1

+

𝐿𝐿

2

𝑠𝑠𝐸𝐸𝐸𝐸

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)} ×

𝑑𝑑𝑋𝑋

𝑖𝑖

𝑑𝑑𝑡𝑡

+ {

𝐿𝐿

1

𝑦𝑦𝐸𝐸𝑠𝑠 𝜃𝜃

1𝑖𝑖−1

+

𝐿𝐿

2

𝑦𝑦𝐸𝐸𝑠𝑠

(

𝜃𝜃

1𝑖𝑖−1

+

𝜃𝜃

2𝑖𝑖−1

)} ×

𝑑𝑑𝑌𝑌

𝑖𝑖

𝑑𝑑𝑡𝑡 �

 

 
 

 

Содержание RAA3064002GFP

Страница 1: ...control Reducing the reference kit s size by integrating the mechanical and electrical structures Integral structures with the control boards installed at the opposite ends of the stepping motors from...

Страница 2: ...URL https www renesas com us en application home building motor control solutions resolver motor control solutions consumer and industrial applications videos This document explains the system configu...

Страница 3: ...Inc Contact MinebeaMitsumi for detailed specifications 42 mm square board 42 mm square motor control board An RX24T is incorporated as the MCU Not for sale 85 mm square board 85 mm square motor contr...

Страница 4: ...on of the Control Coordinate System 32 2 3 Basic Manipulation 33 2 3 1 Procedure for Operations 33 2 3 2 List of Commands and APIs 34 2 3 3 Output Format of output_state 35 2 3 4 List of Parameters 36...

Страница 5: ...Reference Guide for a 2 Axis Robot Arm with 2 Phase Stepping Motors Incorporating Resolvers RX24T RX72M RAA3064002GFP RAA3064003GFP 3 2 2 Registration of Work Origin 57 3 2 3 Training 58 3 2 4 Demonst...

Страница 6: ...ed to the tip of arm 2 and the laser light produces illumination in the direction of the ground The 42 mm square board and 85 mm square board are installed for the 42 mm square motor and 85 mm square...

Страница 7: ...r for arm 1 Origin sensor for arm 2 Laser module Laser 3 V power supply for the laser module 42 mm square motor control board RX72M USB Ethernet Communications Modbus communications at 2 Mbps with the...

Страница 8: ...d mechanical and electrical structures manufactured by MinebeaMitsumi This motor is used for driving arm 2 For the model number and detailed specifications contact MinebeaMitsumi Contact URL https www...

Страница 9: ...st of Components of the Demo System 2 2 Classification Name Description Related Files PC PC for GUI PC for a GUI used to execute demonstrations For operating the GUI the following requirements have to...

Страница 10: ...rd and 85 mm square board for the motors with the corresponding dimensions An MCU 64 pin RX24T and RDC IC both made by Renesas Electronics are mounted on both of them and the 2 phase stepping motors w...

Страница 11: ...driver with built in FET DRV8844 manufactured by Texas Instruments Inc Pressure resistance 60 V Rated current 1 75 A RMS UCC27282 manufactured by Texas Instruments Inc pressure resistance 120 V Drive...

Страница 12: ...f 42 mm square board Figure 1 5 shows the external appearance of the 42 mm square board Figure 1 5 External Appearance of 42 mm Square Board RDC RX24T RDC IC PreDrv FET DC DC LDO VDD AVDD PRG RMW Reso...

Страница 13: ...re Board Item Function Pin in ascending order of pin number from pin 1 Connector Shape Power source Power input GND V 2 54 mm pitch 2 pin Motor Motor output A A B B 2 0 mm pitch 4 pin Communication Pr...

Страница 14: ...TXD6 O UART I F DI signal of RS485 transceiver RS485 22 RXD6 I UART I F RO signal of RS485 transceiver RS485 24 POE4 I Overcurrent signal Overcurrent sensing 26 27 MTIOC7A I RDC I F COUT signal RDC 28...

Страница 15: ...2 Phase Stepping Motors Incorporating Resolvers RX24T RX72M RAA3064002GFP RAA3064003GFP Table 1 4 MCU Pin Assignment 42 mm Square Board 2 2 Pin No Pin Name I O Function of Connected Signal Connection...

Страница 16: ...appearance of 85 mm square board Figure 1 8 shows the external appearance of the 85 mm square board Figure 1 8 External Appearance of 85 mm Square Board 85 mm square board RDC RX24T RDC PreDrv FET DC...

Страница 17: ...Board Item Function Pin in ascending order of pin number from pin 1 Connector Shape Power source Power input GND V 3 5 mm pitch 2 pin Motor Motor output A A B B 1 mm 4 Communication Program E1 or E2 L...

Страница 18: ...C I F SCLK signal RDC 21 TXD6 O UART I F DI signal of RS485 transceiver RS485 22 RXD6 I UART I F RO signal of RS485 transceiver RS485 24 POE4 I Overcurrent signal Overcurrent sensing 26 27 MTIOC7A I R...

Страница 19: ...mm square board of the demo system Control of the positions of the motors is based on the resolver feedback signals and position references from the NC board For details on algorithms for controlling...

Страница 20: ...dled upon receiving operation instructions from a GUI running on the PC and position references of the motor are sent to the 42 mm square board and 85 mm square board which are connected via RS485 The...

Страница 21: ...pposite end of the driving end of the motor axis The 42 mm square board is installed for the 42 mm square motor and the 85 mm square board is installed for the 85 mm square motor Each of the motors an...

Страница 22: ...solvers RX24T RX72M RAA3064002GFP RAA3064003GFP Table 1 7 Main Motor Specifications Item 42 mm Square Motor 85 mm Square Motor Rated voltage V 24 24 Rated current A 2 3 Holding torque Nm 0 5 2A 4 4 1A...

Страница 23: ...4 RE00MU BASE_PLATE Mechanical processed product created based on drawings 1 Lid of cylindrical case 5 RE00MR LOAD_SHAFT Mechanical processed product created based on drawings 1 Part for installing t...

Страница 24: ...B Frame cap for aluminum extrusion MISUMI Group Inc 2 Frame cap for arm 1 19 HFC5_2040_B Frame cap for aluminum extrusion MISUMI Group Inc 2 Frame cap for arm 2 20 SCB6 20 Hex socket head cap screw st...

Страница 25: ...bination of arms 1 and 2 The swing speed of each arm is in a one to one relationship with the rotation speed of the motor because each combination of arm and motor forms a gearless direct drive Though...

Страница 26: ...on a PC without having to be installed The necessary conditions for running on a PC are as follows Supporting OS Windows 7 32 bit or 64 bit version Windows 8 1 32 bit or 64 bit version and Windows 10...

Страница 27: ...ly for the NC board see Renesas Starter Kit for RX72M User s Manual R20UT4391 Note that since some of the 42 mm square board s connection pins are used in common with the debugger and RMW the two cann...

Страница 28: ...E in emulator Not used 6 RES RESET RES in emulator Not used Table 1 13 Connection between the 42 mm Square Board and 24 V Power Supply 42 mm Square Board Power Supply 24 V Power Supply Pin No Pin Name...

Страница 29: ...phase Cos 3 XAP 0 phase Sin 4 XAN 180 phase Sin 5 EXC Excitation Excitation Table 1 18 Connection between the 85 mm Square Board and Emulator 85 mm Square Board Program Emulator Pin No Pin Name Name...

Страница 30: ...ame Meaning 1 GND GND GND 2 B Z B Differential communication line B 3 A Y A Differential communication line A 4 NC Not used Table 1 22 Connection between the 85 mm Square Board and Origin Sensor 85 mm...

Страница 31: ...licable Conditions and Functions The applicable conditions for the NC software are as follows Two degrees of freedom two axes The angle of the arm joints can be sensed by the sensors The singularity o...

Страница 32: ...e rotation direction Table 2 1 Definition of the Control Coordinate System Name Description Motor origin The arm s sensor position corresponding to encoder angles of 0 The coordinates are to be calcul...

Страница 33: ...tes and Offset 1 Turn on the power of the system Disabled 2 Turn on the servo GUI button Disabled 3 Move the motor origin setup_motorzero Disabled 4 Turn off the servo GUI button Disabled 5 Move the a...

Страница 34: ...otorzero joint 1 joint 2 SMZ Returns to the motor origin If the joint 1 0 or 1 or joint 2 0 or 1 argument is set to 1 return to the origin proceeds joint 1 and joint 2 cannot be specified at the same...

Страница 35: ...r MST NG LST NG loop_end MEN LEN Finishes continuous operation Normal MEN OK LEN OK Error MEN NG LEN OK Interrupt operation interrupt_stop IST Stops operation of the arm the instruction that was input...

Страница 36: ...ctory_MAX_ERROR_ CORRECTION 0 to 255 2 R W Offset 1 2 1 degrees Trajectory_OFFSET_1 Trajectory_OFFSET_2 180 to 180 1 0 2 0 Disabled PTP mode 2 Maximum speed RPM Api_PTP_MAXSPEED 0 to 65 535 100 R W Ac...

Страница 37: ...No Error Condition A 1 A response was received during broadcasting A 2 A timeout has occurred because a response could not be received A 3 The CRC in the received response does not match A 4 The funct...

Страница 38: ...tion determination end bit of the 1 bit tangent point data is 0 B 6 When confirming the state of the RX24T before applying CP control the during return to origin bit of the 1 bit tangent point data is...

Страница 39: ...A CP control position reference value was sent in a mode other than CP control mode Exception code 1 A PTP control position reference value was sent in a mode other than PTP control mode Exception cod...

Страница 40: ...1 Calculations for Interpolation Calculate coordinates for interpolating the coordinates in motion between two points Linear interpolation Assuming the velocity is V_X or V_Y and the trajectory veloc...

Страница 41: ...for calculation as follows 1 xc 2 1 2 2 2 xc 2 2 2 2 Since they are a pair of simultaneous quadratic equations there are two solutions clockwise CW trajectory and counterclockwise CCW trajectory For a...

Страница 42: ...he obtained central coordinates 1 2 1 2 2 1 2 2 2 2 2 2 3 2 3 2 2 3 Calculate under the condition that equation 1 is equal to equation 2 1 2 1 2 2 2 2 2 1 1 2 1 2 1 2 2 1 2 0 Similarly calculate under...

Страница 43: ...ing count 1 1 1 On the assumption of the input is X and the output is Y the following is obtained Y 1 1 1 Y 1 1 Initial value Y 0 1 0 1 2 1 The initial values are the XY coordinate values of the posit...

Страница 44: ...erential equation on the assumption of M 4 t 0 Initial value Y 0 1 4 0 1 2 3 t 1 Y 1 0 1 4 1 3 1 4 1 0 1 2 t 2 Y 2 1 1 4 2 2 1 4 2 1 0 1 t 3 Y 3 2 1 4 3 1 1 4 3 2 1 0 t 4 Y 4 3 1 4 4 0 1 4 4 3 2 1 n M...

Страница 45: ...in 1 2 sin 1 2 y 1 cos 1 2 cos 1 2 Differentiate them by time 1 cos 1 2 cos 1 2 1 2 cos 1 2 2 1 sin 1 2 sin 1 2 1 2 sin 1 2 2 Change them into a matrix 1 cos 1 2 cos 1 2 2 cos 1 2 1 sin 1 2 sin 1 2 2...

Страница 46: ...sin 1 2 sin 1 2 1 cos 1 2 cos 1 2 1 1 2 cos 1 sin 1 2 2 2 cos 1 2 sin 1 2 2 1 sin 1 cos 1 2 2 2 cos 1 2 sin 1 2 2 sin 1 2 2 cos 1 2 1 sin 1 2 sin 1 2 1 cos 1 2 cos 1 2 1 1 2 cos 1 sin 1 2 2 1 sin 1 c...

Страница 47: ...e Jacobian calculations Calculate the coordinates X Y from the joint angle of successive Jacobian calculation results X L1 sin 1 2 sin 1 2 Y L1 cos 1 2 cos 1 2 Calculate the error between the obtained...

Страница 48: ...before a timeout 99 s Figure 2 4 Time Chart Typ Figure 2 5 Time Chart Max Trajectory calculation Communication 79 commands 0 s Create transmit data 3 s Response processing 15 s 424 s 25 s Calculate t...

Страница 49: ...ulation CMT0 Cycle of sync command in CP control mode CMT1 Intervals of 2 characters of Modbus communication CMT2 Intervals of 1 5 characters of Modbus communication CMT3 General timeout 1 CP control...

Страница 50: ...detection Low level of RXD6 pin Data length 8 bits Parity Disabled Stop bit 1 bit Data transfer direction LSB first Transfer speed Transfer clock Internal clock Bit rate 115200 bps Bit rate modulation...

Страница 51: ...n use Noise filter Used Hardware flow control Disabled Data match detection Disabled Data processing Processing of transmit data Processed in interrupt service routine Processing of receive data Proce...

Страница 52: ...cy ICLK 240 MHz PCLKA 120 MHz SCI10 PCLKB 60 MHz SCI6 CMT0 to CMT3 TMR0_TMR1 Board RTK5572MNDC00000BJ IDE e2 studio V7 7 0 Compiler CC RX V3 02 00 Emulator E1 emulator 2 7 2 Configuration Image The fi...

Страница 53: ...d or 85 mm square board and write the sample software for driving each of the motors RX24T_ROBOT42_STM_RSLV_FOC for the 42 mm square board and RX24T_ROBOT42_STM_RSLV_FOC for the 85 mm square board 2 A...

Страница 54: ...peak and an antiresonance peak are present record the frequency of each peak If multiple resonance points are visible record the resonance frequencies in the same manner Note that if you do not have a...

Страница 55: ...reference to the guideline for setting the parameters which is shown in Table 3 1 Table 3 1 Guideline for Setting of Resonance Suppressing Filter Setting Item Argument Resonance Frequency is Lower th...

Страница 56: ...2 2021 Reference Guide for a 2 Axis Robot Arm with 2 Phase Stepping Motors Incorporating Resolvers RX24T RX72M RAA3064002GFP RAA3064003GFP R_MTR_SRFOC_SetTorqFilterParam MTR_ID_A 2 2 300 1 10 R_MTR_SR...

Страница 57: ...ction to the NC board 1 Connect the NC board and an emulator and write the NC software RobotArm_rx72m mot to the NC board 2 After software has been written disconnect the emulator from the NC board an...

Страница 58: ...ommand in the GUI and then write the desired operations based on the coordinates that were read out Saving the input command in a text file allows omission of the trouble of re training by reading the...

Страница 59: ...t Arm with 2 Phase Stepping Motors Incorporating Resolvers RX24T RX72M RAA3064002GFP RAA3064003GFP Example Trajectory operation of numeral 8 Figure 3 6 Training for the Trajectory of Numeral 8 Example...

Страница 60: ...24T RX72M RAA3064002GFP RAA3064003GFP 3 2 4 Demonstrations The demo system can execute the training operations with the method shown in Figure 3 8 Another method is to read a text file to which the tr...

Страница 61: ...on In such a case issue a reset When using the move_xxx command to stop operation setting the end flag to 0 makes the motor operate with acceleration so vibration will occur The position is shifted fr...

Страница 62: ...62 Jan 22 2021 Reference Guide for a 2 Axis Robot Arm with 2 Phase Stepping Motors Incorporating Resolvers RX24T RX72M RAA3064002GFP RAA3064003GFP Revision History Rev Date Description Page Summary 1...

Страница 63: ...ut signal during power off state as described in your product documentation 4 Handling of unused pins Handle unused pins in accordance with the directions given under handling of unused pins in the ma...

Страница 64: ...ALL WARRANTIES EXPRESS OR IMPLIED WITH RESPECT TO THIS DOCUMENT AND ANY RELATED OR ACCOMPANYING SOFTWARE OR HARDWARE INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS...

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