An Incremental Approach For Generating Composite Configuration Space Of Polyhedron Part Assembly

In addition to meeting the requirements for properties in mechanics, the mechanicalsystems need to achieve predetermined behavioral functions implemented by the movementof the systems. However, at the design stage, although CAD models can reflect thecomposition and structure of the systems, they can not directly express the system behaviorsthat may be conducted by the real systems made from the models. Actually, for the CADmodels representing a mechanism with variable topology, it is difficult for designers tocompletely predict the comprehensive real behaviors of the models. For example, thereachability between the different target locations is not obvious because of motionuncertainty. Therefore, behavior predictions for system models is important, which can helpdesigners to detect and avoid the wrong designs, optimize the system motion paths, check therealization of predetermined functions, and facilitate the operation planning.To study mechanical behaviors of the assembly models, firstly the concept of compositeconfiguration space (Composite Configuration Space, CCS) is proposed to represent themechanical assembly system behaviors. Two basic elements of the CCS are the configurationparameters and the domains of the parameters. From face-face contact relationship andmotion geometry, a strict definition of contact state of assembly model is given in this paper.Contact state reflects the contacts between all parts in the assembly, and thus it determines therelative motions between any two parts, through which the movements of the system can beparameterized. The system behaviors are divided into two levels, namely the parameter valuechange within a domain and the parameter transformation between different parameterdomains. The two levels of parameter changes can cause contact-state transitions. When theparameters change within the parameter domain, the system parameters are in a continuousconfiguration space where a region is corresponding to a contact state, and the change of thecontact-state determines the boundaries of parameter definition domains. In addition,parameter mapping relations between the parameter domains as well as the properties of theCCS are elaborated.Then, as a preliminary research work on automatic generation of assembly’s CCS, thispaper presents an incremental approach for generating configuration space of polyhedron partassembly. This approach starts with a pair of contact parts as the initial sub-assembly,incrementally updates the CCS as a part is added into the sub-assembly while thesub-assembly changes accordingly. The loop won’t end until all parts of the assembly areadded. Finally, several examples are presented and the steps for generating CCSs of theassembly models are elaborated, which shows some aspects of the feasibility, effectivenessand applicability of the research.