Problems of optimal design of mechanisms are formulated in a state space setting that allows treatment of general design objectives and constraints. A constrained multi-element technique is employed for velocity, acceleration, and kineto-static analysis of mechanisms. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions involving kinematic, force, and design variables. A generalized steepest descent optimization algorithm is employed, using the design sensitivity analysis methods developed, as the basis for a general purpose kinematic system optimization algorithm. Two optimal design problems are solved to demonstrate effectiveness of the method.