The Spatial Peg–in–Hole Problem

In this paper the modeling and simulation of a rectangular peg{in{hole insertion carried out by a six axis manipulator is presented. The dynamic model of the robot coupled with the assembly process model is established, where all possible contact points between the peg and the environment are monitored. Every occurring contact point represents a geometrical constraint on the robots dynamic which is then characterized by closed loops. The contact laws are formulated as a Linear Complementarity Problem (LCP), which allows the determination of the contact forces for dependent constraints. No assumptions about the sequence of the contact points have to be made in advance, rather the sequence results from the time evolution of the system, which depends on the initial conditions. Through the simulation we are able to predict the behavior of the manipulator during the task as well as the load on the mating parts. The comparison with measurements show that this approach is capable of describing the regarded process rather realistically.