# Constraint-wrench analysis of robotic manipulators

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## Abstract

The constraint-wrench analysis of mechanisms, with focus on parallel robots, is the subject of this paper. Although the method proposed here can be generalized for parallel robots with multiple-loop kinematic chains, here, single-loop chains are targeted. To this end, a novel representation of the constraints imposed by the kinematic pairs is introduced. With this representation, the *constraint matrix* of a mechanism is readily derived. For the calculation of the constraint wrenches, by means of the constraint matrix and based on the Newton–Euler formulation, a new procedure is introduced. As a case study, the constraint wrench analysis of the McGill Schönflies Motion Generator (SMG), while undergoing a test cycle adopted by the industry, is conducted.

## Keywords

Constraint-wrench analysis Parallel robots Constraint matrix Newton–Euler formulation Schönflies motion generators (SMG)## Notes

### Acknowledgements

The authors would like to thank Canada’s Natural Sciences and Engineering Research Council (NSERC) for providing funds to support this research via an *Idea to Innovation Grant*, which allowed the team to produce the experimental platform motivating the work reported here. Further work has been supported under NSERC’s *Discovery Grants* program and partly through a James McGill Professorship to the second author.

## References

- 1.Staicu, S., Carp-Ciocardia, D.C.: Dynamic analysis of Clavel’s delta parallel robot. In: Proc. of the 2003 IEEE Int. Conference on Robotics and Automation, Taipei, Taiwan, September 14–19 (2003) Google Scholar
- 2.Choi, H.B., Konno, A., Uchiyama, M.: Inverse dynamic analysis of a 4-dof parallel robot h4. In: Proc. of 2004 IEEE/RJS Int. Conference on Intelligent Robots and Systems, Sendai, Japan, September 28–October 2 (2004) Google Scholar
- 3.Miller, K.: Dynamics of the new uwa robot. In: Proc. 2001 Australian Conferences on Robotics and Automation, Sydney, Australia, November 14–19 (2001) Google Scholar
- 4.Pang, H., Shahinpoor, M.: Inverse dynamics of a parallel manipulator. J. Robot. Syst.
**11**(8), 693–702 (1994) MATHCrossRefGoogle Scholar - 5.Li, Y., Qingsong, X.: Dynamic analysis of a modified delta parallel robot for cardiopulmonary resuscitation. In: Proc. 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), Edmonton, Canada, August 2–6 (2005) Google Scholar
- 6.Staicu, S.: Matrix modeling of inverse dynamics of spatial and planar parallel robots. Multibody Syst. Dyn.
**27**(2), 239–265 (2012) MathSciNetMATHCrossRefGoogle Scholar - 7.Khalil, W., Ibrahim, O.: General solution for the dynamic modeling of parallel robots. J. Intell. Robot. Syst.
**49**, 19–37 (2007) CrossRefGoogle Scholar - 8.Angeles, J., Lee, S.: The modelling of holonomic mechanical systems using a natural orthogonal complement. Trans. Can. Soc. Mech. Eng.
**13**, 81–89 (1989) Google Scholar - 9.Angeles, J.: Fundamentals of Robotic Mechanical Systems Theory, Methods, and Algorithms. Springer, New York (2007) MATHCrossRefGoogle Scholar
- 10.Roth, B.: Screws, motors, and wrenches that cannot be bought in a hardware store. In: Brady, M., Paul, R.P. (eds.) Robotics Research. The First International Symposium, pp. 679–693. MIT Press, Cambridge (1984) Google Scholar
- 11.Klein, F.: Ueber liniengeometrie und metrische Geometrie. Math. Ann.
**V**, 257–303 (1871) Google Scholar - 12.Hartenberg, S., Denavit, J.: Kinematic Synthesis of Linkages. McGraw-Hill, New York (1964) Google Scholar
- 13.Hervé, J., Sparacino, F.: Star, a new concept in robotics. In: Proc. 3rd Int. Workshop on Advances in Robot Kinematics, Ferara, Italy, September 7–9, pp. 176–183 (1992) Google Scholar
- 14.Wohlhart, K.: Displacement analysis of the general spatial parallelogram manipulator. In: Proc. 3rd Int. Workshop on Advances in Robot Kinematics, Ferara, Italy, September 7–9, pp. 104–111 (1992) Google Scholar
- 15.Hervé, J.: The mathematical group structure of the set of displacements. Mech. Mach. Theory
**29**(1), 73–81 (1994) CrossRefGoogle Scholar - 16.Morozov, A., Angeles, J.: The mechanical design of a novel Schönflies motion generator. Robot. Comput.-Integr. Manuf.
**23**, 82–93 (2007) CrossRefGoogle Scholar - 17.Blajer, W., Schiehlen, W., Schirm, W.: A projective criterion to the coordinate partitioning method for multibody dynamics. Appl. Mech.
**64**, 86–98 (1994) MATHGoogle Scholar - 18.Bayo, E., Ledesma, R.: Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics. Nonlinear Dyn.
**9**, 113–130 (1996) MathSciNetCrossRefGoogle Scholar - 19.Zahariev, E., Cuadrado, J.: Dynamics of over-constrained rigid and flexible multibody systems. In: 12th IFToMM World Congress, Besançon, France, June 18–21 (2007) Google Scholar
- 20.Pahl, G., Beitz, W., Feldhusen, J., Grote, K.H.: In: Wallace, K., Blessing, W. (eds.) Engineering Design. A Systematic Approach. Springer, London (2007) Google Scholar
- 21.Gauthier, F., Angeles, J., Nokleby, S.: Optimization of a test trajectory for Scara systems. Adv. Robot Kinemat. Anal. Des.
**4**, 225–234 (2008) CrossRefGoogle Scholar