Perfect static balancing using Cardan-gear spring mechanisms

Publication Name

Mechanism and Machine Theory


This paper presents the static balancing designs (i.e., gravity compensation) for a rotating link by using a special straight-line geared mechanism with springs. The design scenario is to attach the rotating link yet to balance onto an inverted Cardan gear mechanism which has linear springs installed for balancing the weight of the links. It is found that the whole mechanism can be perfectly balanced in theory through either one or two linear springs. The significance of the proposed designs is that the derived solutions for perfect balancing are general. That is, (1) all the masses of the mechanism links are taken into account in the calculation for balancing, (2) the geometry of the design is formulated through the real-spring model (i.e., not zero-free-length springs), (3) the use of compression or extension springs is thoughtfully discussed, and (4) the installation points, preloaded lengths, initial tensions, and stiffness of the springs are considered altogether in the design process. Based on the original design, several design variations are suggested as well. Applications of the design for balancing two special robotic manipulators are illustrated. Last, an experimental test on a prototyped one-DoF balancer was performed.

Open Access Status

This publication is not available as open access



Article Number