平面机构自由度求解中低副高代去除轨迹点重合虚约束

针对平面机构自由度求解中轨迹点重合的虚约束问题，提出低副高代的虚约束去除方法。对轨迹点重合的虚约束在平面运动副中的存在情况进行分析，以椭圆仪机构和齿轮直线机构为例，对其存在的位置进行分析，并进一步研究去除该虚约束的机构方案。结果表明：若平面机构中存在轨迹点重合的虚约束，该轨迹点重合的虚约束并不存在于某个固定的运动副上；在两构件距离不变的两点间加入构件和运动副类虚约束是轨迹点重合虚约束的特例；在不减少构件数目的情况下可以采用将转动低副变成平面高副，去除轨迹点重合虚约束。

Removal of Redundant Constraints of Trajectory Coincidence by Substituting Lower Pair Mechanism by Higher Pair Mechanism in the Calculation of Degree of Freedom in Planar Mechanisms

Aiming at the redundant constraints of trajectory coincidence in the calculation of degree of freedom in planar mechanisms, substituting lower pair mechanism by higher pair mechanism method is proposed to remove them. The existence of redundant constraints of trajectory coincidence in revolute pair, prismatic pair and planar higher pair is analyzed. Taking elliptic mechanism and gear-linear mechanism as examples, the locations of redundant constraints of trajectory coincidence in mechanism pairs are analyzed, and the design of the mechanism scheme without the redundant constraints further studied. The results suggest that if there are redundant constraints of the trajectory coincidence in planar mechanism, the constraints do not exist on a fixed pair; the redundant constraint caused by adding a link with two revolute pairs at two points on two different links with fixed distance is an special case of the redundant constraints of the trajectory coincidence; without reducing the number of links, the redundant constraints of trajectory coincidence can be removed by changing the revolute pair into the planar higher pair.