Elastic Deformation Theories Of Parallel Mechanics Based On CAD Variation Geometric Approach

Stiffness and elastic deformation theories gradually become important subjects in thestudy of Parallel Mechanisms(PMs). There are two traditional methods in stiffness solvingand elastic deformation analysis of PMs, one is analytic method characterized by deducingstiffness matrix，the other is FEA methods characterized by model discretization. The twomethods have their own merits. Based on the advantages of both methods, this thesisfocuses on an analysis of the stiffness and the elastic deformation of the 3/6-SPS PM and3-SPR PM by a novel CAD variation geometric approach.Based on CAD variation geometric approach, inverse and forward position solutionsof 3/6-SPS and 3-SPR PM are solved. By contrasting the inverse position solutions solvedby the analytic approach, the results obtained by CAD variation geometric approach areverified correctly. Based on force-torque balancing equations, the force Jacobian matrix isderived and the force simulation mechanism is constructed in CAD software. According tothe force Jacobian matrix and the force simulation mechanism, active/constrained forcecan be solved automatically. By contrasting the force solutions solved by the analyticapproach and motion analysis module in CAD software, the results obtained by CADvariation geometric approach are verified correctly.According to the knowledge of material mechanics, the elastic deformation of limbsare solved and the equivalent length of limbs are calculated. Based on CAD variationgeometric approach, the position mechanism of PMs after deformation is rebuilt, thus, theposition and posture changes of moving platform can be solved. The stiffness matrix isderived and the elastic deformation is solved by the analytic approach. The solid model isbuilt in CAD software, and the deformation of PMs also can be solved by FEA method.By contrasting the elastic deformation solutions solved by the analytic approach and theFEA method, the results obtained by CAD variation geometric approach are verifiedcorrectly.Based on CAD variation geometric approach, the elastic deformation of 3/6-SPS PMand 3-SPR PM working in some different conditions under different loads is calculated,according to the deformation results, it can be find that the position and posture of moving platform and the loads have a huge influence on the stiffness of PMs. According tocomparing the deformation in different conditions, the change of stiffness can be knownand the influence of forces and torques in different directions can be solved.