基于螺旋理论的正方形单元及其组合机构瞬时自由度分析

Instantaneous Mobility Analysis of Square Unit and Its Combined Mechanism Based on Screw Theory

正方形单元机构在运动过程中,瞬时自由度会发生变化,从而导致其不能继续运动或者运动失稳,或构件损坏等严重后果,因此判别机构自由度的瞬时性和真实性是十分必要的。依据正方形单元及其组合机构的几何特性,基于螺旋理论和图论提出了该类机构瞬时自由度计算的新方法,对比传统的自由度计算公式,该方法可以更真实地反映机构在运动过程中的实际自由度,借助MATLAB仿真证实了该方法的正确性。并结合摄动理论解决了该类机构运动过程中自由度变化的问题,为该类机构运动控制奠定了理论基础。

During movement process, the instantaneous it cannot moving, motion instable, components damage mobility of square unit mechanism will change, then cause or other serious consequence, thus it is necessary to deter- mine the temporariness and truthfulness of mobility. Based on screw theory and graph theory, and according to the geometric features of square unit and its combined mechanisms, this paper presented a new method to calculate in- stantaneous degrees of freedom for such kind of mechanisms. Contrast with traditional calculation formula for degrees of freedom, the presented method could actually reflect the real degrees of freedom during mechanism＇s moving process. This paper verify the correctness of such method with the assistance of MATLAB simulation, moreover, co- operate with perturbation theory, solve the variation problem of degrees of freedom during mechanism＇s moving process, and pave the theory foundation for the motion control of such kind of mechanisms.