一类6-SPS相似平台并联机构正运动学的简明解

6-SPS相似 Stewart平台是一种动、静平台均为平面六边形 ,且彼此相似的并联机构。并联机构正运动学是一个位置和姿态耦合的复杂非线性问题 ,难以求得解析解。通过引入四元数来表示旋转变换和应用对偶空间方法对高阶多项式进行降阶处理 ,可以用一组二阶方程来表示该类并联机构的正运动学。在这组方程中 ,动平台的位置和姿态是解耦的。此外 ,在方程组求解过程中 ,能避免产生伪复根。最后通过求根公式直接得到机构动平台位姿的 8个解析解

CONCISE SOLUTION OF FORWARD KINEMATICS ANALYSIS OF PARALLEL MECHANISM IN 6-SPS SIMILAR PLATFORM

The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however, there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.