| This dissertation formulates and solves the algebraic design equations for five degree-of-freedom articulated chains that generalize the planar RR chains used in mechanism synthesis theory. Planar RR chains are characterized by the requirement that the moving pivot lies on a circle around the fixed pivot, and they introduce one degree of constraint to the end-effector movement. Here our focus is on spatial chains that are characterized by the requirement that the center of a spherical wrist lies on a surface, which constrains the end-effector to one degree-of-constraint, or five degrees-of-freedom. These chains, and parallel systems constructed from them, are called "constrained robotic systems."; The synthesis problem begins with a task defined as a set of goal positions for the end-effector of the chain. These positions can be viewed as an approximation of the workspace desired for the system. Because the spherical wrist allows all orientation of the end-effector, the focus is on the set of points traced by the wrist center, called the "reachable surface." Seven constrained serial chains and their associated reachable surfaces are identified. They are denoted: PPS (plane), TS (sphere), RPS (hyperboloid), CS (cylinder), PRS (elliptic cylinder), right RRS (circular torus), and RRS (torus).; Design equations for each of these chains can be obtained from the equations of the associated surface. The result is a set of polynomial equations that range from total degree 32 for the PPS chain (plane) to over 4 million for the general RRS chain (torus). For simple cases, we use sparse matrix resultant method to obtain analytical solutions. For more complicated cases, a new polynomial homotopy solver POLSYS_GLP is developed and adapted to parallel computer systems. For example the case RRS12 has 42,786 roots and required 45 minutes on 1024 processors of the San Diego Supercomputer Center's Blue Horizon system.; Finally, the analysis and synthesis routines are packaged into a Java and OpenGL based computer-aided design environment called SYNTHETICA . The Java-based architecture has been designed to allow user-collaborators to integrate new synthesis routines into the system using dynamic binding. A general purpose kinematics solver for constrained robotic systems has been developed to simulate their movement. The result is a versatile high level synthesis and simulation system for articulated serial and parallel chains. |
