Design of planar static balancer with associated linkage

• Conversion rules are obtained considering an associated linkage.
• Deletion rules of the design equation are obtained from the conversion rules.
• A new gravity compensator is simply achieved by the deletion rules.

This paper presents a design method for a static balancer with associated linkage. Various mechanisms can be obtained with modifications to the associated linkage. Gravity compensators for various mechanisms can be achieved similarly from a gravity compensator for the associated linkage. The space mapping method is adopted to design a gravity compensator for the associated linkage. Conversion rules are derived by investigating the variances of a mechanism from the associated linkage and are applied to the design equation for the associated linkage generated by the space mapping method. Rows and columns of the design equation are deleted by conversion rules, leading to deletion rules. A new gravity compensator for the mechanism derived from the associated linkage is obtained by applying the deletion rules to the design equation (i.e., gravity compensator) for the associated linkage. The four-bar mechanism is adopted as the associated linkage, and various gravity compensators for planar mechanisms are derived from the gravity compensator of the four-bar linkage. Simulations are conducted, and the results show that complete gravity compensation is possible for various planar mechanisms.