CAJ | 학술논문

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.
6-SPS상사Stewart평태시일충동、정평태균위평면륙변형,차피차상사적병련궤구.병련궤구정운동학시일개위치화자태우합적복잡비선성문제,난이구득해석해.통과인입사원수래표시선전변환화응용대우공간방법대고계다항식진행강계처리,가이용일조이계방정래표시해류병련궤구적정운동학.재저조방정중,동평태적위치화자태시해우적.차외,재방정조구해과정중,능피면산생위복근.최후통과구근공식직접득도궤구동평태위자적8개해석해.
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.