It is well known that the friction force can lead to the analysis complexity of the contact constraint model. Based on Coulomb’s frictional model and unilateral constraint model, non-rigid bodies’ compliant dynamic model was established. Considering the whole motion of the assembly system and elastic contact deformation caused by assembly forces, the nearly rigid contact analysis is proposed. Jamming and wedging must be avoided for successful robot assembly operation. Based on the compliant dynamic model the conditions for jamming and wedging are provided in the formulations of the constrained dynamic system of peg-in-hole insertion.