We describe a parameter 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. This is an important class of systems and is not addressed by prior synthesis research. Kinematic function is computed from the CAD models of the parts and is represented graphically as configuration spaces. Design flaws appear as incorrectly shaped contact curves, as incorrectly placed intersection points, and as incorrect curve sequences. The designer reshapes the faulty curves with the keyboard mouse. The synthesis algorithm computes new parameter values that realize the changes without harmful side effects, using a novel form of constrained optimization. The algorithm has been tested on industrial applications.