On the End-Point Deflection of Static Balanced Manipulators With Various Spring Configurations

This paper presented the accumulation deflection of manipulator with different spring configuration. Spring configurations achieve perfect static balance but they are different in deflection. Assuming the axial deflection is enough smaller than bending deflection and negligible; deflection is small and the link is rigid. Based on gravitational and elastic matrix, for most effective balancing, attachment angles of a spring are determined as four types (90, 0), (270, 90), (0,0) and (180,180). Attachment lengths of a spring are determined by magnitude of gravitational energy. Then, spring force, reaction force and deflection are determined. For illustrated examples, a given manipulator with configuration 4-1 S₂₃ (180,180), S₂₃ (0,0) and 4-2 S₃₄ (180,180), S₃₄ (0,0), the accumulation deflection in global workspace and maximum, minimum and RMS accumulation deflection are presented. In conclusion, the spring configuration 4-1 with S₂₃ (180,180) is the best choice for designers.