Solution of inverse geometrico-static problem (IGP) for suspended rigid-flexible coupling parallel mechanism (RFCPM) driven by elastic thin rods

Abstract. Rigid-flexible coupling is the development trend of lightweight parallel mechanisms. Different from traditional rigid parallel mechanisms, although the flexible components are light in weight, the large elastic deformation generated by the mechanism will affect the precision and stability of the movement. The elastic deformation of the flexible components makes the kinematic modeling challenging, which limits the application and promotion of such mechanisms. To solve the kinematic problems of such mechanisms and improve motion accuracy, this paper takes the rigid-flexible coupling parallel mechanism driven by elastic thin rods as the research object, proposes an inverse geometrico-static problem (IGP) solution, and conducts relevant motion tests to verify the correctness of the solution. Firstly, to solve the geometric relationship between the elastic thin rods and the end of the mechanism during the motion of the mechanism, the rigid-flexible coupling parallel mechanism driven by the elastic thin rods is rigidified and equivalent to a four-cable traction parallel robot, and the rationality of the rigidification equivalence is analyzed. Secondly, the kinematic/static coupling problem (geometrico-static problem) of the four-cable parallel robot is solved by the numerical iteration method, and a simulation example is analyzed, which shows that the cable length and Euler angle are cosine-like functions, the center of gravity distance is negatively correlated with the Euler angle amplitude, and the height and gravity of the end effector are independent of it. Thirdly, for the inverse kinematics problem of the rigid-flexible coupling parallel mechanism driven by elastic thin rods, a method combining the planar chain beam model and the kinematic model of the four-cable parallel robot is proposed. Finally, two experimental platforms are built to test and verify the accuracy of the above kinematic models. The test of the four-cable robot shows that the Fréchet distances of the target trajectories and the actual trajectories are relatively small (near 1), and the test of the rigid-flexible coupling parallel mechanism shows that the maximum errors between the target trajectories and the actual trajectories are all no more than 1.5 mm. The results all indicate that the target trajectories and the actual trajectories are highly consistent, which proves that the models and numerical iterative method are highly accurate. The method proposed in this paper can effectively solve the IGP of similar mechanisms and provide theoretical support for its practical application.