平面广义Stewart平台位置正解求解策略及仿真

Strategies and simulation of direct kinematics for a planar generalized Stewart platform

与六自由度并联机构相比,三自由度并联机构结构简单、易于控制、制造成本低,发展前景广阔。并联机构位置正解研究可为机构的设计提供必要的依据,然而到目前为止,Stewart平台位置正解的求解问题还未彻底解决。采用基于图论的自由度分析法和基于吴消元法的符号计算方法,研究了平面广义Stewart平台的位置正解求解策略。先将平面广义Stewart平台的位置正解问题转化为约束图,再对约束图进行完整约束完备化,生成构造序列,降低同时求解的方程组规模,并用吴消元法求得方程组对应的闭形解。最后对平面广义Stewart平台位置正解进行了基于MapleSim软件的仿真,用实例验证了方法的有效性。

The three-degrees-of-freedom parallel mechanism has broad prospects for development due to its simple structure,easy control and low manufacturing cost compared with the six-degrees-of-freedom parallel mechanism.The direct kinematics of a parallel mechanism is one of the most important issues for parallel kinematic mechanisms. However,to date,the problem of direct kinematics of a Stewart platform has not been completely solved. In this work,strategies for applying direct kinematics to a planar generalized Stewart platform have been illustrated according to graph theory with analysis of degrees of the freedom and a symbolic computation method based on Wu＇s elimination. The problem of direct kinematics for a planar generalized Stewart platform is transformed into a constraint graph. In order to reduce the scale of solving equations simultaneously,the under-constrained constraint graph is completed to make it well-constrained and acquire a construction sequence. Subsequently,the equation system of each construction sequence is solved with Wu＇s elimination method to obtain the closed form solution. Finally,the corresponding simulation is performed using Maple Sim software. The effectiveness of the method is verified by experiments.