A geometric approach to the singularity analysis of in-parallel robot manipulators

This thesis presents a methodology for the singularity analysis of in-parallel manipulators based on the geometry of linearly dependent sets of lines. A wide class of in-parallel manipulators are identified that have pure force contact between the serial-chain support members and the moving platforms. The Jacobian of these systems is shown to consist of screws which represent lines in six dimensional space. The conditions under which the Jacobian loses rank are exactly the geometric configurations of linearly dependent sets of lines.; We summarize the geometric configurations available for linearly dependent sets of lines, termed Linear System of Lines (LSL). The geometric approach to singularity analysis consists of comparing these model configurations to those available to a specific in-parallel manipulator. The result is a classification of singularities of the systems. This procedure is demonstrated in detail for an in-parallel planar manipulator as well as for the spatial 6-6 and 4-6 Stewart platforms.