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A Conceptual and Straightforward Approach for Solving the Closed-form Direct Kinematics of a General Coplanar 6-PUS Parallel Manipulator

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

The proper synthesis of simulators is critical as they allow trainees to experience dangerous maneuvers. The most widely used simulator is the Stewart platform. However, this structure is costly and therefore alternative structures should be considered. The 6-PUS robot is an excellent alternative to the well-known Stewart, thanks to its inherent benefits. Considering the many existing studies on parallel robots, specifically the Stewart robot, there exists a few research on the 6-PUS structure. The comprehensive kinematic analysis of any robot is a prerequisite for robotic engineers. Therefore, to analyze the 6-PUS structure, first, a general kinematic architecture of the 6-PUS robot is defined, in which all actuators are located on a plane connected to the ground. To solve the closed-form direct kinematics, a highly computational efficient elimination method is selected and a detailed stepwise approach is presented which results in a great reduction of the univariate polynomial degree without using the greatest common divisor method. Thanks to its simplicity of implementation and straightforward approach of the presented algorithm, it is theoretically worthwhile in the kinematics analysis of robots. The presented stepwise and conceptual approach to kinematic analysis is general and can be applied to other parallel structures.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Amir Tehrani & Alireza Akbarzadeh

  2. Department of Mechanical Engineering, University of Bojnord, Bojnord, Iran

    S. Nader Nabavi

  3. Department of Mechanical Engineering, Sadjad University, Mashhad, Iran

    Hadi Kalani

Authors
  1. Amir Tehrani
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  2. S. Nader Nabavi
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  3. Alireza Akbarzadeh
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  4. Hadi Kalani
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Corresponding author

Correspondence to Hadi Kalani.

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We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Appendices

Appendix A

See Fig. 

Fig. 8
figure 8

The flowchart of analytical solution of direct kinematics

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8

Appendix B

Figure 

Fig. 9
figure 9

The design parameters of the 6-PUS robot, a Top view of the base platform, b isometric view of the base platform, c top view of the 6-PUS robot, d front view of the 6-PUS robot

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9 shows eight kinematic parameters that describe a general architecture of the 6-PUS robot. These parameters are defined as follows:

  • \(r_{b}\): Base platform radius

  • \(d_{b}\): Distance between \(\overline{{A_{i} A_{j} }}\)

  • \(\beta\): First angular parameter of the slider’s direction

  • \(\gamma\): Second angular parameter of the slider’s direction

  • \(p_{0}\): Initial position of the sliders when the robot is in neutral position

  • \(r_{p}\): Moving platform radius

  • \(d_{p}\): Distance between two spherical joints

  • \(Z_{h}\): Distance between the moving platform and the base platform when the robot is in neutral position

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Tehrani, A., Nabavi, S.N., Akbarzadeh, A. et al. A Conceptual and Straightforward Approach for Solving the Closed-form Direct Kinematics of a General Coplanar 6-PUS Parallel Manipulator. Iran J Sci Technol Trans Mech Eng 47, 753–764 (2023). https://doi.org/10.1007/s40997-022-00545-6

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  • DOI: https://doi.org/10.1007/s40997-022-00545-6

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