Analysis of Constraint Singularities of a 2-DOF Spatial Parallel Mechanism

This paper considers the kinematic analysis of a 2 dof closed-loop chain for the night-sky observation known as the Canterbury tracker. Closed-loop mechanisms are characterized by a higher number of joints than dofs, so kinematic constraints act to make dependent their configurations. For some configurations of the joints, it is possible that one or more constraints become redundant, giving instantaneously extra dofs to the mechanism. Thus, conventional input-output singularities do not represent the unique possibility of having controllability issues. In this paper, the screw theory is exploited to determine singular configurations of the proposed trackers. According to the results of this analysis, the geometric parameters of the mechanism are chosen to make it suitable for solar tracking purpose, taking into account the existence of these singular configurations to avoid tracking failures.