Abstract
A statically-balanced mechanism can remain in indifferent equilibrium at a continuous set of poses while the actuators exert zero work, as the links’ weight is resisted by conservative balancing forces. This can be achieved, for example, by adding counterweights or springs. Studies on gravity balancing frequently target parallel robots, to increase their intrinsic advantages of high stiffness and smaller motor size. Here, it is considered how to balance a 3-DoF kinematic chain for applications on parallel robots, such that the chain generates a constant force on the end-effector. The design does not include counterweights and has most of the auxiliary balancing elements on the fixed base, thus reducing the inertia of moving elements; the motion is transmitted through a lightweight system of gears, pulleys and synchronous belts. The design also leaves greater freedom in the selection of the spring, which (unlike most previous works) may have nonzero free length.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In the following, for brevity, universal joints are denoted by U, prismatic ones by P, rotary ones by R and spherical ones by S; a line over a letter denotes that the corresponding joint is actuated.
- 2.
- 3.
In [5], however, the R joints at \(L_{1u}\) and \(L_{1l}\) (and at \(L_{2u}\) and \(L_{2l}\)) coincided, due to space constraints. Here, a distance \(d=\Vert L_{1u}-L_{1l}\Vert =\Vert L_{2u}-L_{2l}\Vert \) is set, equal to the free length of the auxiliary spring. One can show, then, that the linkage is kinematically equivalent [2] to the pantograph in [5], as link 5 can only translate along axis \(y_0\); thus, the spring need not be ZFL.
- 4.
In the rest of this Section, all rotations are measured with respect to axis \(y_1\), fixed on link 1.
References
Martini, A., Troncossi, M., Carricato, M., Rivola, A.: Static balancing of a parallel kinematics machine with linear-delta architecture: theory, design and numerical investigation. Mech. Mach. Theory 90, 128–141 (2015). https://doi.org/10.1016/j.mechmachtheory.2015.03.003
Barents, R., Schenk, M., van Dorsser, W.D., Wisse, B.M.: Spring-to-spring balancing as energy-free adjustment method in gravity equilibrators. J. Mech. Des. 133(6), 061010 (2011). https://doi.org/10.1115/1.4004101
Kim, H.S., Song, J.B.: Multi-DOF counterbalance mechanism for a service robot arm. IEEE/ASME Trans. Mechatronics 19(6), 1756–1763 (2014). https://doi.org/10.1109/TMECH.2014.2308312
Mottola, G., Cocconcelli, M., Rubini, R., Carricato, M.: Gravity balancing of parallel robots by constant-force generators. In: Gravity Compensation in Robotics. Mechanism and Machine Science, vol. 115, pp. 229–273. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-95750-6_9
Martini, A.: Development of an elastically compensated UPS-type constant-force generator for the static balancing of spatial parallel mechanisms. In: Ascione, L., et al. (eds.) Proceedings of the XXIII AIMETA Conference, pp. 541–549, Salerno, Italy (2017). https://cris.unibo.it/handle/11585/609738
Martini, A.: Gravity compensation of a 6-UPS parallel kinematics machine tool through elastically balanced constant-force generators. FME Trans. 46(1), 10–16 (2018). https://doi.org/10.5937/fmet1801010M
Li, Y., Wang, J., Liu, X.J., Wang, L.P.: Dynamic performance comparison and counterweight optimization of two 3-DOF parallel manipulators for a new hybrid machine tool. Mech. Mach. Theory 45(11), 1668–1680 (2010). https://doi.org/10.1016/j.mechmachtheory.2010.06.009
Baradat, C., Arakelian, V.H., Briot, S., Guegan, S.: Design and prototyping of a new balancing mechanism for spatial parallel manipulators. J. Mech. Des. 130(7), 072305 (2008). https://doi.org/10.1115/1.2901057
Lessard, S., Bigras, P., Bonev, I.A.: A new medical parallel robot and its static balancing optimization. J. Med. Dev. 1(4), 272–278 (2007). https://doi.org/10.1115/1.2815329
Dehkordi, M.B., Frisoli, A., Sotgiu, E., Bergamasco, M.: Modelling and experimental evaluation of a static balancing technique for a new horizontally mounted 3-UPU parallel mechanism. Int. J. Adv. Robot. Syst. 9(5), 193 (2012). https://doi.org/10.5772/54009
Carabin, G., Scalera, L., Wongratanaphisan, T., Vidoni, R.: An energy-efficient approach for 3D printing with a Linear Delta Robot equipped with optimal springs. Robot. Comput. Integr. Manuf. 67, 102045 (2021). https://doi.org/10.1016/j.rcim.2020.102045
Idà, E., Nanetti, F., Mottola, G.: An alternative parallel mechanism for horizontal positioning of a nozzle in an FDM 3D printer. Machines 10(7), 542 (2022). https://doi.org/10.3390/machines10070542
Carricato, M., Gosselin, C.M.: A statically balanced Gough/Stewart-type platform: conception, design, and simulation. J. Mech. Rob. 1(3), 031005 (2009). https://doi.org/10.1115/1.3147192
Ebert-Uphoff, I., Gosselin, C.M., Laliberté, T.: Static balancing of spatial parallel platform mechanisms-revisited. J. Mech. Des. 122(1), 43–51 (2000). https://doi.org/10.1115/1.533544
Wang, J., Gosselin, C.M.: Static balancing of spatial three-degree-of-freedom parallel mechanisms. Mech. Mach. Theory 34(3), 437–452 (1999). https://doi.org/10.1016/S0094-114X(98)00031-7
Gosselin, C.M., Vollmer, F., Côté, G., Wu, Y.: Synthesis and design of reactionless three-degree-of-freedom parallel mechanisms. IEEE Trans. Robot. Autom. 20(2), 191–199 (2004). https://doi.org/10.1109/TRA.2004.824696
Wu, Y., Gosselin, C.M.: Synthesis of reactionless spatial 3-DoF and 6-DoF mechanisms without separate counter-rotations. Int. J. Robot. Res. 23(6), 625–642 (2004). https://doi.org/10.1177/0278364904044400
Gosselin, C.M., Laliberté, T., Mayer-St-Onge, B., Foucault, S., Lecours, A., Duchaine, V., Paradis, N., Gao, D., Menassa, R.: A friendly beast of burden - a human-assistive robot for handling large payloads. IEEE Robot. Autom. Mag. 20(4), 139–147 (2013). https://doi.org/10.1109/MRA.2013.2283651
Briot, S., Arakelian, V., Guégan, S.: PAMINSA: a new family of partially decoupled parallel manipulators. Mech. Mach. Theory 44(2), 425–444 (2009). https://doi.org/10.1016/j.mechmachtheory.2008.03.003
Mottola, G., Gosselin, C.M., Carricato, M.: Effect of actuation errors on a purely-translational spatial cable-driven parallel robot. In: IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), pp. 701–707. IEEE, Suzhou, China (2019). https://doi.org/10.1109/CYBER46603.2019.9066627
Simionescu, I., Ciupitu, L., Ionita, L.C.: Static balancing with elastic systems of DELTA parallel robots. Mech. Mach. Theory 87, 150–162 (2015). https://doi.org/10.1016/j.mechmachtheory.2014.11.008
van Dam, T., Lambert, P., Herder, J.L.: Static balancing of translational parallel mechanisms. In: Proceedings of the ASME 2011 IDETC/CIE, vol. 6, pp. 883–889. ASME, Washington DC, USA (2011). https://doi.org/10.1115/DETC2011-47525
Nguyen, V.L., Lin, C.Y., Kuo, C.H.: Gravity compensation design of Delta parallel robots using gear-spring modules. Mech. Mach. Theory 154, 104046 (2020). https://doi.org/10.1016/j.mechmachtheory.2020.104046
Streit, D.A., Shin, E.: Equilibrators for planar linkages. J. Mech. Des. 115(3), 604–611 (1993). https://doi.org/10.1115/1.2919233
Streit, D.A., Chung, H., Gilmore, B.J.: Perfect equilibrators for rigid body spatial rotations about a Hooke’s joint. J. Mech. Des. 113(4), 500–507 (1991). https://doi.org/10.1115/1.2912811
Walsh, G.J., Streit, D.A., Gilmore, B.J.: Spatial spring equilibrator theory. Mech. Mach. Theory 26(2), 155–170 (1991). https://doi.org/10.1016/0094-114X(91)90080-N
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Mottola, G., Martini, A. (2023). A Novel Spatial 3-DoF Constant-Force Generator for the Static Balancing of Parallel Robots. In: Okada, M. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2023. Mechanisms and Machine Science, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-031-45705-0_73
Download citation
DOI: https://doi.org/10.1007/978-3-031-45705-0_73
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-45704-3
Online ISBN: 978-3-031-45705-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)