An efficient method for computing the forward kinematics of binary manipulators

Binary actuators have only two discrete states (denoted `0´ and `1´), both of which are stable without feedback. As a result, manipulators built with binary actuators have a finite number of states. Compared to a manipulator built with continuous actuators, a binary manipulator provides good performance, and is also relatively inexpensive. However, the number of states of a binary manipulator grows exponentially with the number of actuators. While this makes the calculation of its inverse kinematics quite difficult, the discrete nature of a binary manipulator makes it possible to compute its forward kinematics more efficiently than for a continuously actuated manipulator. By pre-computing all possible configurations of each module of a binary manipulator (a finite and usually small number) it is possible to compute the forward kinematics from a set of joint parameters without using any transcendental functions