Solution of geometrico-static problems and motion experiments for a suspended under-constrained parallel mechanism driven by two flexible cables

The suspended parallel mechanism, due to the use of gravity as a virtual rope to provide both geometric and force constraints, leads to coupled kinematics and statics of the mechanism (geometrico-static), whose under-constrained relationship makes the coupled kinematic/hydrostatic solution very challenging. In order to solve its geometrico-static problem, this paper proposes an inverse kinematic solution algorithm and conducts an experimental study on the equilibrium configuration of the end of the two-rope robot. First, the geometric constraint equations of the force system are derived from the force system equilibrium conditions. Second, motion simulation of the end of the mechanism is carried out to analyze its motion characteristics. Finally, the trajectory similarity between the motion control test and the theoretical calculation is compared. The experimental results show that the solution algorithm proposed in this paper has high accuracy and solution efficiency.