Two Spherical Three Degrees of Freedom Parallel Robots 3-RCC and 3-RRS Static Analysis
The main purpose of this study is static analysis of
two three-degree of freedom parallel mechanisms: 3-RCC and 3-
RRS. Geometry of these mechanisms is expressed and static
equilibrium equations are derived for the whole chains. For these
mechanisms due to the equal number of equations and unknowns, the
solution is as same as 3-RCC mechanism. A mathematical software is
used to solve the equations. In order to prove the results obtained
from solving the equations of mechanisms, the CAD model of these
robots has been simulated and their static is analysed in ADAMS
software. Due to symmetrical geometry of the mechanisms, the force
and external torque acting on the end-effecter have been considered
asymmetric to prove the generality of the solution method. Finally,
the results of both softwares, for both mechanisms are extracted and
compared as graphs. The good achieved comparison between the
results indicates the accuracy of the analysis.
[1] G. O. Young, "Synthetic structure of industrial plastics (Book style with
paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15–64.
[2] H. McCallion, and D. T Pham. "The analysis of a six degree of freedom
work station for mechanized assembly." Proc. 5th World Congress on
Theory of Machines and Mechanisms. Vol. 611. 1979.
[3] K. H. Hunt, "Structural kinematics of in-parallel-actuated robot-arms."
Journal of Mechanical Design 105.4 (1983): 705-712.
[4] C. Gosselin, "Determination of the workspace of 6-DOF parallel
manipulators." Journal of Mechanical Design 112.3 (1990): 331-336.
[5] E. F. Fichter, "A Stewart platform-based manipulator: general theory
and practical construction." International Journal of Robotics Research,
1986, 5(2), 157.
[6] D. E. Whitney, "Force feedback control of manipulator fine motions."
Transactions of ASME, Journal of Dynamic Systems, Measurement and
Control, 1972, Dec, 303±309.
[7] S. Bhattacharya, H. Hatwal, and A. Ghosh. "Comparison of an exact and
an approximate method of singularity avoidance in platform type
parallel manipulators." Mechanism and Machine Theory 33.7 (1998):
965-974.
[8] X. Kong, C.M. Gosselin, "Generation of Parallel Manipulators with
Three Translational Degrees of Freedom using Screw Theory." In
Proceedings of the CCToMM Symposium on Mechanisms 2001.
[9] J. Hervé, "The Lie group of rigid body displacements, a fundamental
tool for mechanism design." Mechanism and Machine Theory, Vol. 34,
No. 5, pp. 719-730, 1999.
[10] X. Kong, C. M. Gosselin, "Type synthesis of 4-DOF SP-equivalent
parallel manipulators: A virtual chain approach." Mechanism and
Machine theory, Vol. 41, No. 11, pp. 1306-1319, 2006.
[11] X. Kong, C. M. Gosselin, "Type Synthesis of Parallel Mechanisms."
Springer, pp. 141-157, 2007.
[12] H. H. Pham, I.-M. Chen, "Kinematics, workspace and static analyses of
a 2-DOF flexure parallel mechanism," In Proceeding of IEEE, 2002, pp.
968-973.
[13] G. Lu, A. Zhang, J. Zhou, S. Cui, L. Zhao, "The Statics Analysis and
Verification of 3-DOF Parallel Mechanism Based on Two Methods."
International Journal of Automation Technology, Vol. 7, No. 2, pp. 237-
244, 2013.
[14] M. T. Masouleh, C. Gosselin, M. H. Saadatzi, X. Kong, H. D. Taghirad,
"Kinematic analysis of 5-RPUR (3T2R) parallel mechanisms."
Meccanica, Vol. 46, No. 1, pp. 131-146, 2011.
[15] M. T. Masouleh, C. Gosselin, M. Husty, D. R. Walter, "Forward
kinematic problem of 5-RPUR parallel mechanisms (3T2R) with
identical limb structures." Mechanism and Machine Theory, Vol. 46,
No. 7, pp. 945-959, 2011.
[16] X. Kong and C. Gosselin. "Type synthesis of parallel mechanisms." Vol.
33. Heidelberg: Springer, 2007.
[1] G. O. Young, "Synthetic structure of industrial plastics (Book style with
paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15–64.
[2] H. McCallion, and D. T Pham. "The analysis of a six degree of freedom
work station for mechanized assembly." Proc. 5th World Congress on
Theory of Machines and Mechanisms. Vol. 611. 1979.
[3] K. H. Hunt, "Structural kinematics of in-parallel-actuated robot-arms."
Journal of Mechanical Design 105.4 (1983): 705-712.
[4] C. Gosselin, "Determination of the workspace of 6-DOF parallel
manipulators." Journal of Mechanical Design 112.3 (1990): 331-336.
[5] E. F. Fichter, "A Stewart platform-based manipulator: general theory
and practical construction." International Journal of Robotics Research,
1986, 5(2), 157.
[6] D. E. Whitney, "Force feedback control of manipulator fine motions."
Transactions of ASME, Journal of Dynamic Systems, Measurement and
Control, 1972, Dec, 303±309.
[7] S. Bhattacharya, H. Hatwal, and A. Ghosh. "Comparison of an exact and
an approximate method of singularity avoidance in platform type
parallel manipulators." Mechanism and Machine Theory 33.7 (1998):
965-974.
[8] X. Kong, C.M. Gosselin, "Generation of Parallel Manipulators with
Three Translational Degrees of Freedom using Screw Theory." In
Proceedings of the CCToMM Symposium on Mechanisms 2001.
[9] J. Hervé, "The Lie group of rigid body displacements, a fundamental
tool for mechanism design." Mechanism and Machine Theory, Vol. 34,
No. 5, pp. 719-730, 1999.
[10] X. Kong, C. M. Gosselin, "Type synthesis of 4-DOF SP-equivalent
parallel manipulators: A virtual chain approach." Mechanism and
Machine theory, Vol. 41, No. 11, pp. 1306-1319, 2006.
[11] X. Kong, C. M. Gosselin, "Type Synthesis of Parallel Mechanisms."
Springer, pp. 141-157, 2007.
[12] H. H. Pham, I.-M. Chen, "Kinematics, workspace and static analyses of
a 2-DOF flexure parallel mechanism," In Proceeding of IEEE, 2002, pp.
968-973.
[13] G. Lu, A. Zhang, J. Zhou, S. Cui, L. Zhao, "The Statics Analysis and
Verification of 3-DOF Parallel Mechanism Based on Two Methods."
International Journal of Automation Technology, Vol. 7, No. 2, pp. 237-
244, 2013.
[14] M. T. Masouleh, C. Gosselin, M. H. Saadatzi, X. Kong, H. D. Taghirad,
"Kinematic analysis of 5-RPUR (3T2R) parallel mechanisms."
Meccanica, Vol. 46, No. 1, pp. 131-146, 2011.
[15] M. T. Masouleh, C. Gosselin, M. Husty, D. R. Walter, "Forward
kinematic problem of 5-RPUR parallel mechanisms (3T2R) with
identical limb structures." Mechanism and Machine Theory, Vol. 46,
No. 7, pp. 945-959, 2011.
[16] X. Kong and C. Gosselin. "Type synthesis of parallel mechanisms." Vol.
33. Heidelberg: Springer, 2007.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70392", author = "Alireza Abbasi Moshaii and Mehdi Tale Masouleh and Esmail Zarezadeh and Kamran Farajzadeh", title = "Two Spherical Three Degrees of Freedom Parallel Robots 3-RCC and 3-RRS Static Analysis", abstract = "The main purpose of this study is static analysis of
two three-degree of freedom parallel mechanisms: 3-RCC and 3-
RRS. Geometry of these mechanisms is expressed and static
equilibrium equations are derived for the whole chains. For these
mechanisms due to the equal number of equations and unknowns, the
solution is as same as 3-RCC mechanism. A mathematical software is
used to solve the equations. In order to prove the results obtained
from solving the equations of mechanisms, the CAD model of these
robots has been simulated and their static is analysed in ADAMS
software. Due to symmetrical geometry of the mechanisms, the force
and external torque acting on the end-effecter have been considered
asymmetric to prove the generality of the solution method. Finally,
the results of both softwares, for both mechanisms are extracted and
compared as graphs. The good achieved comparison between the
results indicates the accuracy of the analysis.", keywords = "Robotic, Static analysis, 3-RCC, 3-RRS.", volume = "9", number = "6", pages = "1092-5", }