Single Exponential Motion and Its Kinematic Generators
Both constant velocity (CV) joints and zero-torsion parallel kinematic machines (PKMs) possess special geometries in their subchains. They are studied as two different subjects in the past literature. In this paper we provide an alternative analysis method based on the symmetric product on \(SE(3)\) (the Special Euclidean group). Under this theoretical framework CV joints and zero-torsion mechanisms are unified into single exponential motion generators (SEMG). The properties of single exponential motion are studied and sufficient conditions are derived for the arrangement of joint screws of a serial chain so that the motion pattern of the resulting mechanism is indeed a single exponential motion generator.
KeywordsConstant velocity transmission Zero torsion Symmetric product Single exponential motion generator
This research is supported by Talents Introduction Startup Funds of High Education of Guangdong Province (2050205) and supported by \(1000\) Young Investigator Plan of the Chinese Government.
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