Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-02T20:15:39.615Z Has data issue: false hasContentIssue false
  • English
  • Français

A geometric approach for the workspace analysis of two symmetric planar parallel manipulators

Published online by Cambridge University Press:  24 July 2014

Banke Bihari ,
Dhiraj Kumar ,
Chandan Jha ,
Vijay S. Rathore  and
Anjan Kumar Dash
Banke Bihari
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Dhiraj Kumar
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Chandan Jha
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Vijay S. Rathore
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Anjan Kumar Dash*
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

The workspace is often a critical parameter for optimum design of parallel manipulators. Workspace shape and area are two important considerations under this. In this paper, 5-R and 3-RRR planar parallel manipulators having symmetric link lengths are considered for workspace analysis. Here, symmetric means that the lengths of the first and second links of the legs are the same in all branches. Workspace analysis for such manipulators is normally done in a nondimensional way. The determination of the workspace area is one of the important parameters in the optimum design of a manipulator, and the determination of the area in terms of nondimensional parameters is extremely difficult in the case of 3-DOF and higher-DOF manipulators. In this paper, a geometric method is presented to determine different workspace shapes and areas. Based on this, all possible shapes of workspace are presented for both 5-R and 3-RRR planar parallel manipulators. For each case, a geometrical relationship between the link lengths is determined. The geometric approach gives a closed-form expression for the area calculation, which is not possible when adopting a nondimensional approach. In addition, this approach provides relationships between workspace shape and area and link lengths.

Keywords

5-R and 3-RRR planar parallel manipulatorsWorkspace shapeWorkspace areaGeometrical approach
Type
Articles
Information
Robotica , Volume 34 , Issue 4 , April 2016 , pp. 738 - 763
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Gosselin, C. M., “Determination of the workspace of 6-DOF parallel manipulators,” ASME J. Mech. Des. 112, 331–336 (1990).CrossRefGoogle Scholar
2.Lee, K. M. and Shah, D. K., “Part 1: kinematic analysis of a 3-DOF in-parallel actuated manipulator,” IEEE J. Robot. Autom. 4, 354–360 (1988).Google Scholar
3.Merlet, J.-P., “Direct kinematic and assembly motion parallel manipulators,” Int. J. Robot. Res. 11 (2), 150–162 (1992).CrossRefGoogle Scholar
4.Merlet, J. P., Gosselin, C. M. and Mouly, N., “Workspace of planar parallel manipulators,” Mech. Mach. Theory 33 (1/2), 7–20 (1998).Google Scholar
5.Cervantes-Sánchez, J. J., Hernández-Rodríguez, J. C. and Rendón-Sánchez, J. G., “On the workspace, assembly configurations and singularity curves of the RRRRR-type planar manipulator,” Mech. Mach. Theory 35, 1117–1139 (2000).Google Scholar
6.Gao, F., Liu, X.-J. and Gruver, W. A., “Performance evaluation of two-degree-of-freedom planar parallel robots,” Mech. Mach. Theory 33 (6), 661–668 (1998).Google Scholar
7.Gao, F., Zhang, X., Zhao, Y. and Wang, H., “A physical model of the solution space and the atlases of the reachable workspaces for 2-DOF parallel plane wrists,” Mech. Mach. Theory 31 (2), 173–184 (1996).Google Scholar
8.Park, F. C. and Kim, J. W., “Singularity analysis of closed kinematic chains,” J. Mech. Des. 121, 32–38 (1999).CrossRefGoogle Scholar
9.Cervantes-Sánchez, J. J., Hernández-Rodríguez, J. C. and Angeles, J., “On the kinematic design of the 5R planar, symmetric manipulator,” Mech. Mach. Theory 36, 1301–1313 (2001).CrossRefGoogle Scholar
10.Alıcı, G. and Shirinzadeh, B., “Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing,” Robotica 22, 97–108 (2004).Google Scholar
11.Alici, G., “An inverse position analysis of five-bar planar parallel manipulators,” Robotica 20, 195–201 (2002).Google Scholar
12.Gao, F., Liu, X.-J. and Chen, X., “The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators,” Mech. Mach. Theory 36, 205–220 (2001).CrossRefGoogle Scholar
13.Liu, X.-J., Wang, J. and Pritschow, G., “Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms,” Mech. Mach. Theory 41, 145–169 (2006).Google Scholar
14.Gao, F., Zhang, X. Q., Zhao, Y.-S. and Wang, H.-R., “A physical model of the solution space and the atlas of the reachable workspace for 2-DOF parallel planar manipulators,” Mech. Mach. Theory 31 (2), 173–184 (1996).Google Scholar
15.Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220–226 (1991).Google Scholar
16.Sen, D. and Singh, B. N., “A geometric approach for determining inner and exterior boundaries of workspaces of planar manipulators,” J. Mech. Des. 130 (2), 022306 (1–9) (2008).CrossRefGoogle Scholar
17.Gallant, A., Boudreau, R. and Galant, M., “Geometric determination of the dexterous workspace of n-RRRR and n-RRPR manipulators,” Mech. Mach. Theory 51, 159–171 (2012).CrossRefGoogle Scholar
18.Saadatzi, M. H., Masouleh, M. T. and Taghirad, H. D., “Workspace analysis of 5-PRUR parallel mechanisms (3T2R),” Robot. Comput. Int. Manuf. 28, 437–448 (2012).Google Scholar
19.Yahya, S., Moghavvemi, M. and Mohammed, H. A. F., “Geometrical approach of planar hyper-redundant manipulators: inverse kinematics, path planning and workspace,” Simul. Model. Prac. Theory 19, 406–422 (2011).Google Scholar
20.Riley, K. F., Hobson, M. P. and Bence, S. J., Mathematical Methods for Physics and Engineering (Cambridge University Press, Cambridge, 2010).Google Scholar