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Direct Kinematics- The Arm Equation

Direct Kinematics- The Arm Equation. Link Coordinates and Kinematics Parameters (Cont‘d) Another example: A 5-axis articulated robot (Rhino XR-3) (refer to class notes for details) Exercise: Determine the link coordinates and the kinematics parameters of the Motoman robot arm

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Direct Kinematics- The Arm Equation

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  1. Direct Kinematics- The Arm Equation Link Coordinates and Kinematics Parameters (Cont‘d) Another example: A 5-axis articulated robot (Rhino XR-3) (refer to class notes for details) Exercise: Determine the link coordinates and the kinematics parameters of • the Motoman robot arm • the SONY arm (LAB-2) COMP322/S2000/L9

  2. The Arm Equation For a n-axis robot arm, the arm equation is P0 = T Pn where P0 is a point (vector) w.r.t. frame L0 , ie. The base frame; Pn is a point (vector) w.r.t. frame Ln, ie. The tool frame; T is the transformation matrix. Question: What is T? T is the composite transformation from one frame to another and is expressed in terms of the kinematics parameters. COMP322/S2000/L9

  3. Arm Equation Consider the transformation from one frame to another, say from frame Lk-1 to Lk. Idea is find the transformation that will bring Lk-1to align with Lk . 4 fundamental motions: First two motions: • Rotate Lk-1 about zk-1to bring xk-1 parallel to xk , ie. by an angle of qk => pure rotation: Rot(qk , zk-1 ) • Translate Lk-1 along zk-1to bring xk-1 align with xk , ie. by a distance of dk => pure translation: Trans(dk , zk-1 ) => Screw (dk , qk , zk-1 ) COMP322/S2000/L9

  4. Arm Equation Second two motions: • Translate Lk-1 along xk-1(xk ) to bring Lk-1 and Lk (the two origins) to coincide, ie. by a distance of ak => pure translation: Trans(ak , xk-1 ) • Rotate Lk-1 about xk-1(xk ) to bring zk-1 to align with zk , ie. by an angle of ak => pure rotation: Rot(ak , xk-1 ) => Screw (ak , ak , xk-1 ) Let Tk-1k denote the transformation from frame Lk-1 to frame Lk, i.e. Pk-1 = Tk-1k Pk COMP322/S2000/L9

  5. Arm Equation Question: • Tk-1k = Screw (dk , qk , zk-1 ) Screw (ak , ak , xk-1 ) = A ? or • Tk-1k = Screw (ak , ak , xk-1 ) Screw (dk , qk , zk-1 ) = B ? Note: Refer to class notes for the details to answer the above question. COMP322/S2000/L9

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