In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to nonlinear equations that are difficult to solve. In particular, the inverse position analysis comprises different subproblems which need specific solution techniques. Finally a numerical example is reported.
Tsai, L. W., 1998, “Systematic Enumeration of Parallel Manipulators,” Proceedings of the 1st European-American Forum on Parallel Kinematic Machines, Milan, Italy, pp. 1–11.
Sternheim, F., 1987, “Computation of the Direct and Inverse Kinematic Model of the Delta 4 Parallel Robot,” Robotersysteme, 3, pp. 199–203.
Clavel, R., 1988, “A Fast Robot With Parallel Geometry,” 18th Int. Symposium on Industrial Robots, Sydney, Australia, pp. 91–100.
Herve`, J. M., and Sparacino, F., 1991, “Structural Synthesis of “Parallel” Robots Generating Spatial Translation,” Fifth ICAR International Conference on Advanced Robotics, June 19–22, Pisa, Italy, pp. 808–813.
Tsai, L. W., 1996, “Kinematics of a three-dof Platform With Three Extensible Limbs,” Recent Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publishers, pp. 401–410.
Tsai, L. W., and Stamper, R., 1996, “A Parallel Manipulator With Only Translational Degrees of Freedom,” ASME 1996 Design Engineering Technical Conference, paper 96-DETC-MECH-1152, Irvine, CA.
N. R., and
A Forward and Reverse Displacement Analysis of an In-Parallel Spherical Manipulator,”
Mech. Mach. Theory,
The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,”
ASME J. Mech. Trans. Aut. Des.,
Echelon Form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist,”
Mech. Mach. Theory,
G. R., and
Position Analysis of a 3-dof Parallel Manipulator,”
Mech. Mach. Theory,
Lee, J. J., and Chang, Sun-Lai, 1992, “On the Kinematics of the UPS Wrist for Real Time Control,” DE-Vol. 45, 22nd ASME Biennial Mechanisms Conference, Robotics, Spatial Mechanisms, and Mechanical Systems, Scottsdale, Arizona, pp. 305–312.
Lee, K. M., and Shah, D. K., 1987, “Kinematic Analysis of a Three Degrees of Freedom In-Parallel Actuated Manipulator,” Proceedings of the 1987 IEEE International Conference on Robotics and Automation, Vol. 1, pp. 345–350.
Padmanabhan, B., Tidwell, P. H., Salerno, R. J., and Reinholtz, C. F., 1992, “VGT-Based Gimbals: Practical Construction and General Theory,” ASME DE-Vol. 47, Flexible Mechanisms, Dynamics and Analysis, pp. 437–443.
Yang, P.-H., Waldron, K. J., and Orin, D. E., 1996, “Kinematic of a Three-Degree-of-Freedom Motion Platform for a Low-Cost Driving Simulator,” Recent Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publishers, pp. 89–98.
Andrisano, A. O., 1990, “Sul Progetto di un Dispositivo di Osteosintesi Esterna,” Atti del sesto Convegno Nazionale ADM (in Italian), pp. 405–416.
Di Gregorio, R., and Parenti-Castelli, V., 1998, “Kinematics of a 6-dof Fixation Device for Log Bone Fracture Reduction,” submitted to J. Intell. Robot. Syst. (JIRS).
Parenti-Castelli, V., and Innocenti, C., 1990, “Direct Displacement Analysis for Some Classes of Spatial Parallel Mechanisms,” Proceedings of the Eight CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Cracow, Poland, pp. 126–133.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland, Amsterdam.
Roth, B., 1993, “Computations in Kinematics,” Computational Kinematics, J. Angeles, G. Hommel, and P. Kovacs, eds., Kluwer Academic Publishers, pp. 3–14.
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