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Direct Kinematics- Link Coordinates

Direct Kinematics- Link Coordinates. Questions: How do we assign frames? At the Joints? At the Links? Denavit-Hartenberg (D-H) Representation Associates frames with links L k is the frame associated with link k,

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Direct Kinematics- Link Coordinates

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  1. Direct Kinematics- Link Coordinates Questions: How do we assign frames? At the Joints? At the Links? Denavit-Hartenberg (D-H) Representation • Associates frames with links • Lk is the frame associated with link k, • Lk= {xk, yk, zk} where xk, yk, zk are orthonormal vectors. • Link(k) is “attached” to the axis xk • Joint(k) connects link(k-1) to link(k) • zkis the axis of motion at the frame Lk • Joint(k) is “attached” to zk-1 COMP322/S2000/L8

  2. Kinematics Parameters • Joint Angle (q ) - the rotational angle about z(k-1)to bring x(k-1)to xk • variable for revolute(rotational) joints • constant for prismatic(translational) joints • Joint Distance (d ) - the translational distance along z(k-1)to bring x(k-1)to intersect with xk • constant for revolute (rotational) joints • variable for prismatic (translational) joints Note: Refer class notes for details and diagrams COMP322/S2000/L8

  3. Kinematics Parameters • Link Twist Angle (a ) - the rotational angle about xkto bring z(k-1)to zk • Link Length (a ) - the translational distance along xkto bring z(k-1)to intersect with zk Both parameters are constants, they are the specifications of the robot. Note: Refer class notes for details and diagrams COMP322/S2000/L8

  4. Link Coordinates For an n-axis robot arm, the 4n kinematics parameter set if the minimal set to specify the kinematics configuration of the arm. By the D-H representation convention, the numbering of joints and links starts at the fixed base which is link 0 ending at the end-effector (the tool), linkn. The Frame at the tool: zn, (roll) - the approach vector, usually align with z(n-1) yn, (pitch) - the sliding vector, usually align with the open-close motion of the tool xn, (yaw) - the normal vector, once zn and yn are determined, xn is determined by the right-hand rule. Note: Refer to class notes for diagrams and details COMP322/S2000/L8

  5. D-H Representation (Algorithm) An algorithm to derive the link coordinates and the kinematics parameters of a robotic arm is given by the reference text (Schilling, Page 54). An example of the Alpha II robotic arm is used. Note: Refer to class notes for diagrams and details COMP322/S2000/L8

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