Abstract: The procees of inserting a peg into a hole is studied in this thesis. There are three stages in a generalinsertion process: 1. chamfer crossing; 2. one point contact; 3. two points contact. The restraint and themovement in these stages had been analysed in detail, and the method of homogeneous coordinate trans-formation had been used in this thesis. The results obtained from these analyses can be used as reference todesign all sorts of compliant wrist, especially passive compliant wrist.