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Kinematic synthesis of spatial mechanisms using algebra of exponential rotation matrices

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2005
Soltani, Fariborz
The major part of this thesis has been devoted to path and motion generation synthesis of spatial mechanisms. For the first time kinematic synthesis methods have been developed based on the algebra of exponential rotation matrices. Besides modeling spatial pairs such as spheric, cylindric and Hook's joints by combinations of revolute and prismatic joints and applying Denavit-Hartenberg's convention, general loop closure equations have been presented for path and motion generation synthesis of any spatial mechanism with lower kinematic pairs. In comparison to the existing synthesis methods the main advantage of the methods presented in this thesis is that, general loop closure equations have been presented for any kind of spatial mechanism with lower kinematic pairs. Besides these methods enable the designer to benefit the advantages of the algebra of exponential rotation matrices. In order to verify the applicability of the synthesis methods presented in this thesis, the general loop closure equations of RSHR, RCCR and RSSR-SC mechanisms have been determined and then using these equations six numerical examples have been solved. Some tables have been presented based on the determined loop closure equations which reveal useful information about the number of precision points or positions that can be considered for the kinematic synthesis of the above mentioned mechanisms and the number of free parameters. In numerical examples, the mechanisms have been synthesized based on the general loop closure equations and the synthesis algorithms presented in the thesis. Although in some cases semi-analytical solutions have been obtained, in most of the cases, the loop closure equations were solved by computer programs written by Mathcad. The input angle-output angle diagrams drawn at the end of each numerical example illustrate the motion continuity of the mechanisms and that