Efficient estimation of the extremal articular forces of a parallel manipulator in a translation workspace

We consider a classical Gough platform with extensible legs whose platform is submitted to a given load. This load induces forces in the linear actuators of the legs, these forces being dependent upon the posture of the platform, and we determine the extremal values of the articular forces when the platform is translating in a given 3D workspace (the orientation of the platform is assumed to be constant). We describe an efficient algorithm which enable one to compute the extremal forces more efficiently than a discretisation method.