9.6
Joint Properties
9.6.1
Encoder to Joint Ratios
This section describes all mechanical reductions in the 262 and 280 hands as well as the ratios that
go from finger and spread encoder positions to joint positions in units of radians. To find the
finger or spread mechanical reduction relative to the motor use the constants in the table below.
Table 10 applies to the hands
before
breakaway occurs. Each finger has 3 joints starting with the
knuckle joint that swings the spread, the last one moves the outer link, and the one in between
moves an amount proportional to the outer link until breakaway occurs. To go from motor
encoder position to actual finger position for joint 2 multiply the encoder position by the
corresponding joint Radians to ticks ratio. Joint 3 of the finger moves one third this amount. This
transformation works
before
breakaway of the TorqueSwitch™ has occurred.
Table 10 - Finger and Spread Joint Ratios
Hand Motor
Encoder
Encoder
Mechanical
Joint Radians/tick
(Min Ticks)
(Max ticks)
Reduction (Joint)
Ratio _
262 Finger
0
17,500
125 (2), 375 (3)
(140°)(π/180°)/17,500
262 Spread
0
3,150
17.5 (1)
π/3,150
280 Finger
0
199,111.1
125 (2), 375 (3)
(140°)(π/180°)/199,111.1
280 Spread
0
35,840
17.5 (1)
π/35,840
The optical encoders for each of the 280 hand motors have 4096 count encoders and 262 hand
motors uses a 90 line, or 360 count, encoder. Inner link encoders are the same ones used on the
motor for position feedback.
The forward kinematics from section 9.5, that are used to calculate end-tip positions, depend on
the configuration of joint positions for each finger (joint 2 and joint 3) and the spread. Calculate
positions in radians for each joint including spread, finger joint 2, and finger joint 3. These will be
the joint positions
before
breakaway.
Joint 3 position can be represented more precisely if it is calculated relative to the plane of the
palm plate that is accurate
before
and
after
breakaway. This position for joint 3 depends only on
the model number (262 or 280) of the hand where
Φ
3
is a joint 3 offset from joint 2 equal to
approximately 42°.
262 Joint 3 Position = (π/180°)(
Φ
3
+ (4/375)ENC(k))
280 Joint 3 Position = (π/180°)(
Φ
3
+ (4/375)ENC(k)(360/4096))
Equation 4 - Joint 3 Positions Before and After Breakaway
Note that joint 1 in the knuckle drives the outer link first through a 93.75 reduction and then a 4:1
reduction. The motor position directly determines the outer link angle with the palm plate of the
hand as shown in Equation 4. During breakaway joint 2 position needs to be detected in software
by using breakaway acceleration threshold for the 262 hand and then this link remains motionless
as described in section 9.3. The breakaway position may be used for finding where breakaway
occurred. Joint 3 position still only depends on just absolute motor position. On 280 hands, the
inner-link joint position sensors may be used together with the outer link position to determine the
finger positions at all times.
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