The synthesis of reactionless mechanisms generally involves the force balancing of a mechanism using countermasses followed by the dynamic balancing of the inertia using counter-rotations. This approach requires that the force balanced mechanism have a constant equivalent moment of inertia for any configuration. Two of the main drawbacks of reactionless mechanisms are a significant increase in mass and actuation inertia. In this paper, a counter-mechanism is introduced in order to dynamically balance a force balanced two-DOF mechanism with variable inertia, which is expected to reduce the aforementioned drawbacks. The conditions for which the counter-mechanism matches the moment of inertia of the main mechanism for any configuration are derived. Then, in order to fairly compare the use of a counter-mechanism instead of counter-rotations, the balancing strategies are optimized regarding the addition of mass and actuation inertia using Lagrange multipliers. The results are optimal rules for the design of reactionless mechanisms and optimal mass-inertia curves which are akin to Pareto curves. These results allow to demonstrate the advantages of counter-mechanisms over counter-rotations, especially regarding added actuation inertia and compactness. Also, the significant influence of the radius of gyration of the counter-inertias on the optimal mass-inertia curves is revealed. Finally, examples of reactionless mechanisms are presented and prototypes are tested in order to validate the concepts.
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The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. 89715) and the Canada Research Chair Program.
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Laliberté, T., Gosselin, C. Synthesis, optimization and experimental validation of reactionless two-DOF parallel mechanisms using counter-mechanisms. Meccanica 51, 3211–3225 (2016) doi:10.1007/s11012-016-0582-0
- Dynamic balancing
- Parallel mechanism
- Reactionless mechanism
- Planar mechanism