In this paper, a Jacobian matrix of the general inline planar platform is studied. An inline planar platform is a manipulator with three legs, each with RPR joints such that the revolute joints are free and align on each platform and the prismatic joints are powered. The configurations that cause the Jacobian matrix to become singular, called the singularity surface, must be avoided for controllability. The Jacobian matrix is developed in the even Clifford algebra Cl(P2) of the projective space P2 and its singularity surface is viewed in a three-dimensional space.

Stacking many platforms on top of one another can make a redundant manipulator. A redundant planar platform manipulator is shown to have a block diagonal Jacobian matrix with block entries the same as the individual planar platform's Jacobian matrix. A composite of singularity sets is developed for the redundant planar platforms. A three-dimensional multi-platform manipulator is looked into as to whether or not it too would have a similar result and a comparison is made to the robotic spherical wrist.

mab3376@tntech.edu