基于卡位分析的曲柄摇杆机构运动学程序化研究

曲柄摇杆机构是典型的平面四杆体机构,当曲柄为从动件时,存在曲柄与连杆共线的歧运动位(卡位或死点),难以实现准确的程序化研究.取曲柄为主动件,对矢量投影方程组多次求导和对角速度多次求导获得了相同的从动件位置角高阶导数.取摇杆为主动件,基于L’Hopital法则、导数乘法法则、链式求导法则和矢量方程图解法,获得了0/0型不定式的卡位运动学参数,并导出了计算公式,从而为准确的运动学程序化仿真打下了基础.算例表明,矢量投影方程组的求导与求解顺序不影响最终结果;在卡位,从动曲柄保持运动的连续性,没有冲击.

On the Programmed Kinematics Computation of Crank Rocker Mechanism Based on the Kinematics Bifurcation Position Analysis

The crank-rocker mechanism is a typical planar quabody mechanism.When the crank is a driven part,there is a kinematics bifurcation position(stuck position or dead point)with the collinear crank and rod.So it is difficult to achieve accurate programmed research.With the crank as the driving part,the same higher derivatives of the driven part position angles were obtained through differentiation of the vector projection equations and the angular velocity formula several times.With the rocker as the driving part,based on the L’Hopital’s rule,the derivative multiplication law,the chain derivative law and the vector equation graphic method,the kinematics parameters of 0/0 indefinites at the stuck position were obtained.The calculation formula was derived.So the foundation for accurate kinematics programmed simulation was made.The example shows that,1)the order of derivation and solution of the vector projection equation system does not influence the final result;2)the driven crank keeps the continuity of motion without impact at the stuck position.