PR2 Gripper Transmission

Basic transmission equations:

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Where

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  gripper gap size

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  motor revolution

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  screw drive

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  intermediate variable.

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  gear ratio

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  geometric constants of the gripper

Jacobians

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where

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Inverse Transform (from $$\theta$$ to $$MR$$)

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where

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and

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Transmissions

Denote

• joint_state->position by $$P_j$$ : gripper gap size in meters

• actuator_state->position by $$P_a$$ : motor angle in radians

• joint_state->velocity by $$V_j$$ : gripper gap velocity in meters per second

• actuator_state->velocity by $$V_a$$ : motor angular rate in radians per second

• joint_state->effort by $$E_j$$ : in Newtons

• actuator_state->effort by $$E_a$$ : motor torque in Newton-Meters

Propagate From Actuator State to Joint State $$(P_a,V_a,E_a) \rarr (P_j,V_j,E_j)$$

Motor angle in radians ($$P_a$$) is converted to motor revolutions ($$MR$$),

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and we have the transmission equation for gripper gap size above

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.

Motor angular rates in radians per second (

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) is converted to revolutions per second,

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and the gripper gap velocity is approximated by

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Given motor torque

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, gripper effort

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is approximated by

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where

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is the moment of inertia at the motor and

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is defined as

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is the motor torque in

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.

Propagate From Joint State to Actuator State $$(P_j,V_j,E_j) \rarr (P_a,V_a,E_a)$$

pretty much the reverse of previous section, given

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, inverse transmission gives

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, and

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.

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Known Limitations

• Gripper transmission produced gripper effort differs from actual measured gripper effort by +/-20%.