Real-time algorithm, based on two extra sensors, for monitoring platform’s orientation of underactuated parallel wrists

The direct position analysis of parallel manipulators (PMs) brings to determine a finite number of platform poses compatible with an assigned set of actuated-joint variables’ values. Therefore, when, during functioning, the need to check the actual platform pose arises, the sensors usually located on the actuators are not sufficient and the additional pieces of information coming from ad-hoc-devised extra sensors are necessary. Here, for the first time, the actual implementation of extra sensors in underactuated parallel wrists (PWs) which contain a nonholonomic constraint is addressed. Differently from ‘‘ordinary’’ (i.e., non-underactuated) PWs, these PWs requires a continuous monitoring of the actual platform orientation to compensate the possible sliding in the nonholonomic constraint. Thus, in this case, the algorithms that interpret the pieces of information coming from the sensors must work in real time and must be integrated in the control software that manages the motion of the machine. All these special requirements are satisfied by the proposed algorithm. Moreover, the proposed hardware can also be implemented in some ordinary PWs with a cheap add-on kit.