A Little Kinematics

Abstract

In Section 3.7, it was stated that the general problem of inverse kinematics for robots is rather difficult. However, for the 3-R wrist it is possible to give a general solution. This is because we are only dealing with three joints, and since the joints are all revolute, intersecting at a single point, we can reduce everything to the rotation group SO(3). So consider a three-joint wrist, as in Figure 5.1, with the joint axes aligned along the unit vectors v₁, v₂ and v₃. These are the home positions of the axes, and we will assume that these vectors are linearly independent. If the home position of the wrist has linearly dependent joint axes, then we can always move it a little and use a non-singular home position.