On the correctness of using two-dimensional representations in the analysis of cylindrical peg–hole insertion and withdrawal

Abstract

The cylindrical peg–hole system is a popular model in the study of assembly and disassembly operations. The analysis of peg–hole systems is customarily performed using simplified two-dimensional representations, viz. a vertical sectional view. However, evidence that this simplification accurately represents the system is lacking. This paper investigates the correctness of using two-dimensional instead of three-dimensional models for peg–hole system analysis, studying their geometrical and kinematic equivalence. Geometrical equivalence implies the contact points between the peg and hole are on a vertical sectional view plane. Kinematic equivalence requires that the forces and torques acting on the peg lie in the same sectional plane. The analysis indicates that while geometrical equivalence can be proven, kinematic equivalence is in general not verified. The severity of the error introduced by the two-dimensional simplification depends on the geometrical configuration and kinematic parameters of the peg–hole system. The effects of kinematic non-equivalence on the boundary conditions of jamming and wedging are discussed. The results of the analysis show that a two-dimensional peg–hole model may give wrong predictions on jamming. Also, the extra lateral error of the three-dimensional model reduces the boundary condition and the possibility of peg–hole wedging.

Keywords

• peg–hole problem
• geometrical equivalence
• kinematic non-equivalence
• simplification
• jamming and wedging
• remote compliance centre