PEG-ON-HOLE: PATTERNS OF MOTION TO ENSURE ALIGNMENT OF PEG WITH VERTICALLY FIXED HOLE DURING AUTOMATED ASSEMBLY
DOI:
https://doi.org/10.32461/2226-3209.3.2018.171926Keywords:
cylindrical parts, three contact points, compound motion, three degrees of freedom, dynamic responses, differential equations.Abstract
Abstract. Automation of assembling cylindrical parts is a currently central problem of the technology of machinebuilding. To address it, assembly devices shall be improved, and software programs for controlling alignment process shall becreated. The ways of improving cylindrical parts assembly operations depend on whether movement of an actuator is in compliance with the objectively defined laws of motion that specify the process of alignment. The paper is aimed at studying peg-
on-hole motion supported at the edge of vertically fixed hole, and creating thereupon a mathematical model for the process of aligning cylindrical parts. The task set was tackled using methods of theoretical mechanics. They enabled to identify common patterns of peg motion with three degrees of freedom and involving planar motion that facilitates the process of aligning parts when nutation angle changes, rotational motion around hole axis characterized with precession angle, and rotational motion
about its axis defined by self-rotation angle. The analysis conducted enabled to find directions of velocities, normal reactions, and friction forces at the contact points. A system of differential equations in generalized coordinates, which we call Dynamic Differential Equations, is created. It is a mathematical model describing the process of aligning cylindrical parts in general terms, and allowing to analyze all possible alternatives of vertical assembly. A particular case of this motion is analyzed when
peg has two degrees of freedom performing planar motion and rotating about its axis. It is found that here the forces acting on the peg at the contact points shall be considerably reduced that improves the conditions for alignment of parts and quality of assembly as well. The equations of one freedom degree motion of a peg served as a basis for developing a method of experimental determination of friction coefficient for assembling certain parts which improves accuracy of finding interaction forc-
es. The results obtained are of practical importance when evaluating and developing methods for assembling, designing assembly devices, imply the ways to improve assembly operations, develop software programs and train Artificial Intelligence for controlling assembly process.
Key words: cylindrical parts, three contact points, compound motion, three degrees of freedom, dynamic responses, differential equations.
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