The robot being considered is a two-degree-of-freedom five-bar planar parallel robot (see Figure 1) for positioning applications. The robotic mechanism consists of a wrist (point P) supported by two articulated arms. Each arm is composed of two links forming a closed chain connected through five revolute (R) joints between the links (at points A and B, P) and to the ground (points O1 and O2). The link lengths of each two-link arm are L and m, respectively. Point Q is the tool center point of end effector which is located at βm from the wrist point P along the upper right arm.
Geometric structure of the planar 5R parallel robot