零耦合度Stewart型并联机器人的位置正解个数

The Number of Forward Position Solutions for Zero Coupling Stewart-Type Parallel Robot

一般六自由度并联机构的位置正解是继空间7R(R:转动副)机构位移分析完成后的又一机构学难题,目前数学上尚无完备的解析求解方法。以零耦合度的“3-2-1”式Stewart型并联机器人为例,研究了位置正解的个数,并分析了正解个数发生变化的条件。首先,基于杆长约束方程并运用四面体原理,解析推导了机器人位置正解的全部8组解。其次,通过分析动球铰的位置特性,挖掘出正解方程分别为8组、4组、2组、1组解析解时,所需满足的数学条件。接着,根据静球铰位置特性并结合正解算法流程,研究了影响正解方程实数解个数的因素。最后,剖析了并联机器人位置正解个数与Hunt奇异之间的内在联系。研究结论为并联机器人的实时控制和轨迹规划奠定了理论基础。

The forward kinematics of a general six-degree-of-freedom parallel mechanism is a significant challenge in mechanism theory,following the displacement analysis of spatial 7R(R:revolute joint)mechanisms.Currently,there is no comprehensive analytical solution available.Using the zero-coupling“3-2-1”Stewart-type parallel robot as an example,this study investigates the number of solutions for the forward kinematics and analyzes the conditions under which the number of solutions varies.First,based on the rod length constraint equations and applying the tetrahedron principle,all eight sets of solutions for the robot’s forward kinematics are analytically derived.Then,by examining the positional characteristics of the moving spherical joints,the mathematical conditions required for the solution equations to yield 8,4,2,or 1 analytical solutions are identified.Furthermore,by considering the positional characteristics of the fixed spherical joints and integrating the forward kinematics algorithm,the factors influencing the number of real solutions are explored.Finally,the intrinsic relationship between the number of solutions to the forward kinematics of the parallel robot and Hunt’s singularities is analyzed.The findings of this research provide a theoretical foundation for the real-time control and trajectory planning of parallel robots.