1. 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

2. The Arm Equation
Thus, for a n-axis robot arm, the transformation matrix becomes
R0n(q) | p0n(q)
T0n(q) =
| 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

3. 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