Governing equations for the dynamics of peg-in-hole insertion for six distinct cases are derived. It is shown that there exist generalized inequalities that govern the processes of successfully inserting a peg in a hole in computer-aided assembly processes. Exact inequalities are obtained for no-wedging and/or no-jamming conditions in computer-controlled dynamic assembly. An algorithm is also described for successful implementation of computer-aided dynamic insertion through the use of optimal trajectories pertaining to the dynamic motion of the peg in the hole.>