The Influence of Motion Path and Assembly Sequence on Stability of Assemblies

Abstract

Abstract-In this paper we present an approach for the stability analysis of mechanical part disassembly considering part motion in the presence of physical forces such as gravity and friction. Our approach uses linear complementarity to analyze stability as parts are moved out of the assembly. As each part is removed from the assembly along a specified path during disassembly, we compute the contact forces between parts in the remaining assembly; positive contact forces throughout the disassembly process imply the disassembly sequence is stable (since the parts remain in contact with one another). However, if the part that is being taken out induces motion of other parts in the remaining subassembly, we conclude the disassembly sequence is unstable. Thus, we are able to simulate the entire disassembly sequence considering physical forces and part motion, which has not previously been done. We then show the influence of part motion on the selection of stable disassembly sequences. In contrast to prior work on disassembly which has focused either on planning part motions based on only geometric constraints, or on analyzing the stability of an assembly without considering part motions, we explore the relation between part motion and the selection of stable disassembly sequences. Since we track the motion of all parts in an assembly, instability inducing motions can be identified and prevented by introducing appropriate fixtures, by selecting alternative disassembly sequences, or by changing the motion paths. We also describe when the presence of physical forces can make assembly and disassembly noninvertible, i.e., disassembly is not the inverse of assembly.

Review and taxonomies of assembly and disassembly path planning problems and approaches

“…Since real-world environments for assembly operations are 3D, only a few researches have modeled their (dis)assembly path planners in 2D [18,[35][36][37]. Nevertheless, when parts are simple 2.5D objects located next to (and not atop of) each other, the problem is better to be modeled in 2D.…”

“…Most assembly path planners use only geometric models of parts and assembly, and plan part motions that are merely collision-and intersection-free, whereas some others consider physical properties of the parts and incorporate factors such as friction [18,23,25,27,29,30,36,[46][47][48], gravity [18,[23][24][25][26][27][28][29][30], and forces [18, 23, 25-28, 30, 36, 46, 48-50] into the problem model, in addition to the geometrical constraints. Nevertheless, no work has been found to deal with the thermal expansion/contraction physical property, as well as mechanical constraints (such as part deformations under tensional, torsional or compressional stresses) in (dis)assembly operations, although sometimes an assembly task is possible only through considering such mechanical behavior of parts.…”

“…Starting from the initial cell of a disassembly path for a subassembly, if an outgoing arc is added to a node of the desired subassembly in the DBG by traversing a particular cell, an alternate route has to be determined [3]. Rakshit and Akella in 2013 used the DBG concept to solve the Motion Stability Problem (introduced in Section 1) in the presence of physical forces such as gravity and friction [18]. As each part is removed from the assembly along a specified path, their method uses linear complementarity (developed in [93]) to analyze stability of parts in the remaining assembly.…”

“…When only geometric constraints are concerned and all parts are rigid, there is a bijection between assembly and disassembly sequences and paths, though this bijection does not remain correct when physics (e.g. gravity, friction) and motion control uncertainty are taken into account, or when some parts are deformable [18] or toleranced [19]. For example, disassembly of a part assembled by rivets is not simply the reverse of its assembly.…”

“…Mosemann et al first created an AND/OR assembly graph in [29] and then analyzed the stability of the subassemblies at each node of the AND/OR assembly graph in [30]. Recently, Rakshit and Akella have presented an approach for the motion stability analysis of mechanical parts disassembly in the presence of physical forces such as gravity and friction [18]. (2) Assembly Maintainability Problem investigates the possibility of removing a particular part from an assembly without changing positions and orientations of other parts, and finds such a path if one exists.…”