Generalized robust systems-based theoretical kinematic inverse/regular wedge cam procedures which produce self-centering motion applicable to three-point clamping device design about cylindrical workpieces that vary within a prescribed size range are presented. Within such presentment, various parametric (trigonometric, combined loop closure with vector projection/resolution, transformation) and rectangular form (Taylor series approximation, trigonometric substitution & transformation (TS&T), nonlinear ODE) equation methods along with related statics and dynamics are explored. In connection, a simulated unified resultant amplitude method (URAM) is applied for generalization purposes. Moreover, the theoretical framework is validated within the context of a computer-generated model of a mechanism design which demonstrates self-centering over the prescribed design range with negligible to zero error. Furthermore, the static and dynamic analyses are verified through computer-aided engineering simulation in conjunction with equilibrium equations and a consideration of various calculus principles. Consequently, the self-centering theoretical formulation coupled with static and dynamic analyses provide for an accurate and generalized quantitative model couched within a holistic systems engineering framework which can be useful for providing state-of-the-art engineering and design optimization of various parameters for developing new and/or improved self-centering gripping devices of the inverse/regular wedge cam type.
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