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Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work

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Abstract

In this research, a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work. For the first time, a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms. An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories. Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.

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Notes

  1. \(\left[ {{\varvec{a}}} \right] _\times =\left[ {{\begin{array}{ccc} 0&{} {-a_z }&{} {a_y } \\ {a_z }&{} 0&{} {-a_x } \\ {-a_y }&{} {a_x }&{} 0 \\ \end{array} }} \right] \),

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Author information

Authors and Affiliations

  1. Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Geelong, VIC, 3217, Australia

    Siamak Pedrammehr, Saeid Nahavandi & Hamid Abdi

Authors
  1. Siamak Pedrammehr
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  2. Saeid Nahavandi
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  3. Hamid Abdi
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Corresponding author

Correspondence to Siamak Pedrammehr.

Appendix

Appendix

Hexarot mechanism specifications:

\(a_{i}\)

\(l_{i}\)

\(s_{1}\)

\(s_{2}\)

\(h_{1}\)

\(h_{2}\)

\(h_{3}\)

\(h_{4}\)

\(h_{5}\)

\(h_{6}\)

0.63

1

0.46

0.06

1.835

1.715

1.335

1.215

0.835

0.715

\(m_{p}\)

\(m_{a}\)

\(m_{l}\)

\(r_{ai}\)

\(r_{li}\)

\({ }^{{P}}I_p \)

\(\bar{{I}}_{aaai} \)

\(\bar{{I}}_{nnai} \)

\(\bar{{I}}_{aali} \)

\(\bar{{I}}_{nnli} \)

5.76

7.62

2.43

0.248

0.493

0.404

0.0168

0.37

1.9\(\times 10^{-4}\)

0.198

  1. Note: All quantities in this table are in SI units

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Pedrammehr, S., Nahavandi, S. & Abdi, H. Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work. Acta Mech. Sin. 34, 883–895 (2018). https://doi.org/10.1007/s10409-018-0761-4

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  • DOI: https://doi.org/10.1007/s10409-018-0761-4

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