This paper introduces several new types of parallel mechanisms with prismatic actuators whose degree of freedom is dependent on a constraining passive leg connecting the base and the platform. A general kinetostatic model is established for the analysis of the structural rigidity and accuracy of this family of mechanisms. The geometric model of this class of mechanisms is first introduced. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, a few examples are given to illustrate the results.

Gough, V., 1956, “Contribution to Discussion to Papers on Research in Automobile Stability and Control and in Tire Performance,” in Proceedings of the Auto. Div. Instn mech. Engrs, p. 392.
Stewart, D., 1965, “A Platform With Six Degrees of Freedom,” in Proceedings of the Institution of Mechanical Engineers, Vol. 180, pp. 371–378.
Pouliot, N. A., Gosselin, C. M., and Nahon, M. A., 1998, “Motion Simulation Capabilities of Three-Degree-of-Freedom Flight Simulators,” AIAA Journal of Aircraft, Vol. 35, No. 1, pp. 9–17.
Advani, S. K., 1998, The Kinematic Design of Flight Simulator Motion-Bases, Delft University Press.
Reinholz, C., and Gokhale, D., 1987, “Design and Analysis of Variable Geometry Truss Robot,” in Proc. 9th Applied Mechanisms Conference, U.S.A.
Arai, T., Cleary, K., Homma, K., Adachi, H., and Nakamura, T., 1991, “Development of Parallel Link Manipulator for Underground Excavation Task,” in 1991 International Symposium on Advanced Robot Technology, pp. 541–548.
Gosselin, C. M., and Hamel, J., 1994, “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” in Proceedings of the IEEE International Conference on Robotics and Automation, pp. 781–786.
Physik-Instrumente, 1997, “Hexapod 6 Axis Micropositioning System,” in Supplement to the Catalog No. 111/112, pp. 36–37.
Lauffer, J., Hinnerichs, T., Kuo, C. P., Wada, B., Ewaldz, D., Winfough, B., and Shankar, N., 1996, “Milling Machine for the 21st Century—Goals, Approach, Characterization and Modeling,” in Proceedings of SPIE—The International Society for Optical Engineering Smart Structures and Materials 1996: Industrial and Commercial Applications of Smart Structures Technologies, Vol. 2721, pp. 326–340, San Diego.
Bailey, P., 1994, “The Merits of Hexapods for Robotics Applications,” in Conference on next steps for industrial Robotics, pp. 11/8–16/8, London.
Hollingum, J., 1997, “Features: Hexapods to Take Over?,” Industrial Robot, Vol. 24, pp. 428–431.
Pritschow, G., and Wurst, K.-H., 1997, “Systematic Design of Hexapods and Other Parallel Link Systems,” CIRP Annals—Manufacturing Technology, Vol. 46, No. 1, pp. 291–295.
Aronson, R. B., 1997, “Hexapods: Hot or Ho Hum?,” Manufacturing Engineering, pp. 60–67.
Matar, G., 1997, “Hexapod: Application-Led Technology,” Prototyping Technology International, pp. 70–72.
Gregorio, R. D., and Parenti-Castelli, V., 1999, “Influence of Leg Flexibility on the Kinetostatic Behavior of a 3-dof Fully-Parallel Manipulator,” in Proceedings of Tenth World Congress on the Theory of Machines and Mechanisms, pp. 1091–1098.
Gosselin, C. M., and Zhang, D., 1999, “Stiffness Analysis of Parallel Mechanisms Using a Lumped Model,” Technical report, De´partment de Ge´nie Me´canique, Universite´ Laval.
Zhang, D., 2000, Kinetostatic Analysis and Optimization of Parallel and Hybrid Architectures for Machine Tools. Ph.D. thesis, Laval University.
Zhang, D., and Gosselin, C. M., 2000, “Kinetostatic Analysis and Optimization of the Tricept Machine Tool Family,” in Proceedings of Year 2000 Parallel Kinematic Machines International Conference.
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