A binary parallel robot manipulator uses actuators which have only two stable states and is structure is variable geometry truss. As a result, it has a finite number of states and fault tolerant mechanism because of kinematic redundancy. This kind of robot manipulator has the following advantages compared to a traditional one. Feedback control is not required, task repeatability can be very high, and finite state actuators are generally inexpensive. Because the number of states of a binary robot manipulator grows exponentially with the number of actuators, it is very difficult to solve an inverse kinematic problem. The goal of this paper is to develop an efficient algorithm to solve an inverse kinematic problem when the number of actuators are too much or the target position is located outside of workspace. The backbone curve is generated optimally by considering the curvature of the robot manipulator configuration and length of link. Then, the robot manipulator is fitted along the backbone curve with some criteria.