This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

本文研究了平面滑块曲柄连杆机构的螺杆坐标中的正向和反向运动学。根据螺杆的定义，刚体的角速度和其上一点的线速度都用螺杆分量表示。通过对速度解的数值积分，我们得到位移。通过速度的数值微分插值，我们可以得到任意关节的加速度。传统上，位置和角度参数通常是建立机构位移方程的唯一变量。对于串联机构，正向运动学可以在位置参数的变量中明确表达，而逆向运动学由于解的多样性而不得不求助于数值算法。对于并联机构，反向运动学可以用末端执行器的位置参数变量来明确表达，而正向运动学由于系统的非线性而不得不求助于数值算法。因此，这肯定会导致用于计算加速度的二阶数值微分插值。这种运动学算法最突出的优点是我们只需要一阶数值微分插值来计算加速度。为了计算位移，我们也只需要速度的一阶数值积分。这种好处源于其坐标是速度分量的螺杆。平面四杆和五杆滑块曲柄连杆的示例验证了该算法。