Computer-aided synthesis of higher pairs via configuration space manipulation

We describe a parametric synthesis algorithm for planar mechanical systems comprised of higher kinematic pairs in which each part translates along a fixed axis or rotates around a fixed point. Kinematic function is computed from the CAD models of the parts and is represented graphically as configuration spaces. The designer uses the mouse to request changes in the configuration spaces. The program computes parameter values that achieve the changes. The computation is iterative: the program repeatedly linearizes the mapping from design parameters to kinematics around the current values, pseudo-inverts the linear mapping, and performs a small parameter modification that moves the system toward the desired kinematics. At each iteration, the program matches the current kinematics against the initial kinematics. If it detects an unintended change, it backs up, adds kinematic constraints that prevent the change, and resumes iteration.