It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable, that is, it might not reproduce a stable motion along a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown through numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the end-effector of the parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained from the tion of the uncontrollable motion. This condition is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated through experimental tests.

The static balancing of mechanical systems is an important issue because it allows one to significantly decrease the size of actuators for equivalent displacements of the end effector. Indeed, the actuators do not have to produce the required input energy to counterbalance the variation of the potential energy of the robot. However, the literature review shows that in many cases the gravity balancing of mechanical systems is carried out by neglecting the masses of auxiliary links associated with the principal mechanism. For many balancing schemes, it is a source of errors.This paper deals with an improved solution for gravity compensators based on the inverted slider-crank mechanism considering the masses of the coupler and the spring. To achieve this, the torques are determined due to auxiliary links. Subsequently, they are introduced into the balancing equation for minimization of the residual unbalance. Hence, a more accurate balancing of gravity compensators based on the inverted slider-crank mechanism can be achieved. The efficiency of the suggested approach is illustrated by numerical simulations.