Question

3 XE 0 0

Determine the Inverse Kinematics Solution for the following robot manipulator

Answer 1

Robot Kinematics: Forward and Inverse Kinematics 121 Example 1 As an example, consider a 6-DOF manipulator (Stanford Manipulator) whose rigid body and coordinate frame assignment are illustrated in Figure 3. Note that the manipulator has an Euler wrist whose three axes intersect at a com- mon point. The first (RRP) and last three (RRR) joints are spherical in shape. P and R denote prismatic and revolute joints, respectively. The DH parameters corresponding to this manipulator are shown in Table 1 Уз x2 yi Figure 3. Rigid body and coordinate frame assignment for the Stanford Manipulator ai-cl αί-1 0 0 h 2102 90 0 d2 -90 0 d 0 0 0 5|05 90 0 0 90 0 0

It is straightforward to compute each of the link transformation matrices using equation 1, as follows. ce,-se, 0 0 0 0 d 0 -10 0 0 0 0 1 0 0 01 c,s, 00 (10) The forward kinematics of the Stanford Manipulator can be determined in the form of equation 3 multiplying all of the T matrices, where i-1,2, ..., 6. In this case, T is given by

32 33 where