differential equations

cylindrical parts

three contact points

complex motion

two degrees of freedom

dynamic reactions

Computer Modeling and Simulations

Machinery, technology and equipment

Scientific and technical research

This paper presents a solution to the problem of a peg leaning on the edge of a horizon-tal hole at three points. The object of the interest is the motion in the course of automated peg-in-hole assembly. The complex motion of a peg is described in two degrees of freedom. These degrees of freedom are planar motion and rotational motion. Planar motion provides parts alignment via a change of nutation angle. Rotational motion occurs around a hole axis. It is described by a precession angle. The kinematic analysis of these was performed. Based on this analysis the directions of the peg velocities at the contact points were established. The directions of forces acting on the peg at these points were also determined. The system of Dynamic Differential Equations of the generalized coordinates was derived. This system determines the equations of the peg motion and dynamic reactions. During rotational motion, the forces acting on the peg at contact points are shown to be significantly reduced. This reduction improves the conditions of parts alignment and increases the assembly quality.