COMP322/S2000/L81 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, L k = {x k, y k, z k } where x k, y k, z k are orthonormal vectors. Link(k) is “attached” to the axis x k Joint(k) connects link(k-1) to link(k) z k is the axis of motion at the frame L k Joint(k) is “attached” to z k-1

COMP322/S2000/L82 Kinematics Parameters Joint Angle (  ) - the rotational angle about z (k-1) to bring x (k-1) to x k –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 x k –constant for revolute (rotational) joints –variable for prismatic (translational) joints Note: Refer class notes for details and diagrams

COMP322/S2000/L83 Kinematics Parameters Link Twist Angle (  ) - the rotational angle about x k to bring z (k-1) to z k Link Length (a ) - the translational distance along x k to bring z (k-1) to intersect with z k Both parameters are constants, they are the specifications of the robot. Note: Refer class notes for details and diagrams

COMP322/S2000/L84 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), link n. The Frame at the tool: z n, (roll) - the approach vector, usually align with z (n-1) y n, (pitch) - the sliding vector, usually align with the open- close motion of the tool x n, (yaw) - the normal vector, once z n and y n are determined, x n is determined by the right-hand rule. Note: Refer to class notes for diagrams and details

COMP322/S2000/L85 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