Direct Kinematics: the Arm Equation (Cont’d) Recall: Link variables (ak , ak) are constants, i.e. characteristics of the arm Joint variables (qk , dk) determine the location of the frame Lk w.r.t. frame Lk-1 Let qk denote the kth joint variable, qk = qk if the kth joint is revolute; and qk = dk if the kth joint is prismatic. Let q denote the vector of joint variables. For the Rhino 5-axis articulated robot arm, q = (q1 , q2 , q3 , q4 , q5 ) For a 4-axis cylindrical robot arm, q = (q1 , d2 , d3 , q4 ) COMP322/S2000/L10

The Arm Equation Thus, for a n-axis robot arm, the transformation matrix becomes R0n(q) | p0n(q) T0n(q) = - - - - - - - - - - - - - 0 0 0 | 1 where R0n(q) is the orientation of the tool frame Lk w.r.t. the base frame L0 p0n(q) is the position of the tool frame Lk w.r.t. the base frame L0 Example: Rhino 5-axis articulated arm (refer to class notes for details) COMP322/S2000/L10

Summary of Direct Kinematics Given the vector of joint variables (q) and the other arm characteristics (e.g. the link constants, ak , ak) of a robot arm and the configuration of the tool tip w.r.t. the frame attached to the tool, the configuration of the tool tip w.r.t. the robot base can be determined. Question: Given the orientation and position of the tool in world coordinates, what are the values of q ? ==> Inverse Kinematics COMP322/S2000/L10