Simplified Torque Modelling for Different Planer Robots Sizes

Previously, many efforts and more time were required to simulate the torque of a robot due to the complicated formulation of the torque. In this paper, simplified equations of the torque for the planar robot are derived. As well as another form of the torque formulation as a Polynomial equation is proposed. The equations of motion for a planar robot have been presented using Lagrange Equation. The proposed derivation of the torque was verified for different sizes of robots (from microscale to large-scale robots). The time simulations of angular displacement, angular velocity, angular acceleration, torque, and power are demonstrated. The robot size effect on the output torque is investigated. The results exhibit an easiness of evaluation of the torque, especially for a robot with a higher degree of freedom. Finally, it is observed the high convergence between the proposed simple formulation and the Lagrange derivation with a maximum error of 0.3 %.