Torque criteria for the stable slow-varying 2-DOF Planar Manipulator Robot (PMR) with identical Stokes damping

DOI

10.2991/978-94-6463-566-9_7How to use a DOI?

Abstract

The main goal of this research is to find torque criteria for the stable 2-DOF planar manipulator robot (PMR) with identical Stokes damping in a slow-varying (SV) regime. The analysis starts by finding the 2-DOF PMR with Stokes damping Equation of Motion (EOM) via the Lagrangian mechanics. In the next step, the SV approximation is applied to those EOMs and produce new EOMs with identical Stokes damping. These SV approximation EOM stability criteria are analyzed using the Jacobian formalism. From the Jacobian formalism, this research found that the SV regime stability criteria for identical Stokes damping do not depend on the value of damping constants. Then, from these stability criteria, this research also found six possibilities of stable eigenvalue regions with the example of PMR link masses M 1 = M 2 = M and PMR link lengths a 1 = a 2 = a . All six stable eigenvalue regions correspond to the interval of the 2-DOF PMR joint angles. In general, those six stable eigenvalue regions are the same, so this research only picked one of the six stable eigenvalue regions, the fifth region. The fifth region leads to the two scenarios of joint angle intervals, { θ 1 ∗ , θ 2 ∗ } = { ( π , 2 π ) , ( - π , 0 ) } ; { ( π , 2 π ) , ( 0 , π ) } . According to those joint angle intervals, the torque criteria for the stable 2-DOF PMR with identical Stokes damping in an SV regime should be { τ 1 ′ , τ 2 ′ } = { ( - 2 M g a , 2 M g a ) , ( - 0.52 M g a , 0.5 M g a ) } a n d { τ 1 ′ , τ 2 ′ } = { ( - 2 M g a , 1.5 M g a ) , ( - 0.5 M g a , 0 ) } .

Copyright

© 2024 The Author(s)

Open Access

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TY  - CONF
AU  - Deriyan Senjaya
AU  - Muhammad Ismail Yunus
PY  - 2024
DA  - 2024/11/01
TI  - Torque criteria for the stable slow-varying 2-DOF Planar Manipulator Robot (PMR) with identical Stokes damping
BT  - Proceedings of the  International Conference on Advanced Technology and Multidiscipline (ICATAM 2024)
PB  - Atlantis Press
SP  - 81
EP  - 98
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-566-9_7
DO  - 10.2991/978-94-6463-566-9_7
ID  - Senjaya2024
ER  -