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Gravity Balancing of Parallel Robots by Constant-Force Generators

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Gravity Compensation in Robotics

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 115))

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Abstract

This Chapter reviews the literature on gravity balancing for parallel robots by using so-called constant-force generators. Parallel robots are formed by several kinematic chains connecting, in parallel, a fixed base to a moving end-effector. A constant-force generator is a mechanism that is able to exert, at a given point, a force having constant magnitude and direction. Gravity balancing of serial robots is a well established technique; conversely, application in parallel robotics is controversial. Indeed, the addition of gravity-balancing mechanisms to a parallel robot may worsen its dynamic behavior, as shown in some referenced works. In this Chapter, we introduce a taxonomy of constant-force generators proposed so far in the literature, including mass and spring balancing methods, toghether with more niche concepts. We also summarize design considerations of practical concern.

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Notes

  1. 1.

    For conciseness, we only consider the most general case of mechanisms having three-dimensional motion; the case of planar motion can be derived as a sub-case, where each frame is defined by only two coordinate axes instead of three.

  2. 2.

    Here, we implicitly assume the springs to be linear. Indeed, some works [25, 31, 32] employ torsional (angular) springs. In this case, the derivation of the potential energy is similar, replacing the stretched and rest lengths by corresponding angles \(\phi _j\) and \(\phi _{j,0}\); the spring stiffness \(k_j\) is then defined in angular units.

  3. 3.

    Notice that the gravity force acting on the EE may vary after the payload is changed; some designs that allow the mechanism to adapt to changes of the EE total weight while keeping the global gravitational balance of the mechanism are reported in Subsect. 5.2.

  4. 4.

    Notice that some authors [50] define instead the shaking force as the total force applied by the fixed ground to the mechanism; a similar notation applies then to the shaking moment.

  5. 5.

    Here and in the following, R denotes a rotary joint, P a prismatic joint, U a universal joint and S a spherical joint; a line above each symbol (such as \(\overline{\mathrm {P}}\)) denotes that a joint is actuated.

  6. 6.

    In this Chapter, we always implicitly assume \(g\ne 0\); indeed, for mass-balanced systems it can be readily seen that the formulas hold for any value of g. Therefore, a mechanism mass-balanced on Earth (\(g=9.80665\,\text {ms}^{-2}\)) retains its properties even in different gravity environments, such as in space or on the surface of other planets; this can be useful for designs targeted for space exploration.

  7. 7.

    Without loss of generality, we assume all angles \(\phi \), \(\psi \), \(\alpha \), \(\beta \) and \(\theta \) to be in the range .

  8. 8.

    Only two springs are employed, for simplicity, but more springs could be introduced; this provides greater freedom in design, but does not significantly change the results shown here. For instance, a spring between links 2 and 0 could be introduced; since link 2 and 1 move at the same angular speed, however, it can be shown that its effect is equivalent to that of a spring between links 1 and 0.

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  1. University of Modena and Reggio Emilia, Via G. Amendola 2, 42122, Reggio Emilia, Italy

    Giovanni Mottola, Marco Cocconcelli & Riccardo Rubini

  2. University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Marco Carricato

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Mottola, G., Cocconcelli, M., Rubini, R., Carricato, M. (2022). Gravity Balancing of Parallel Robots by Constant-Force Generators. In: Arakelian, V. (eds) Gravity Compensation in Robotics. Mechanisms and Machine Science, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-030-95750-6_9

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