Analytical dynamic modeling of Delta robot with experimental verification

Abstract

In this paper, an explicit dynamic model of Delta robot is obtained analytically. The main contribution of this work is that, unlike existing prior work, the final dynamics model is given directly in the form of [Formula: see text], with explicit expressions for M, C and G. This is of great importance, since many advanced control techniques like Optimal Control need dynamic model in an explicit form, i.e. time derivative of state vector given explicitly in terms of the states and control vectors. To this goal, first, velocity and acceleration analysis is done by differentiating robot's geometrical loops directly. Then, Jacobian matrices are calculated to have kinematic relations in a more compact form. After that, principle of virtual work is implemented to derive the dynamic equations. In this part, Jacobian matrices are substituted into dynamic model. This is unlike other referenced works on Delta robot dynamics that need to continue the derivation in symbolic software or derive the model implicitly. Using Jacobians, dramatically simplifies the final explicit dynamic model. Therefore, the final dynamic equations are calculated in a straightforward manner without any use of symbolic calculation software. After all, the presented model is verified with an experimental setup. The model shows good accuracy in terms of torque prediction.

A workload identification method of industrial robot combining dynamic model and convolutional neural network

“…And the impact of the inertia-coupling characteristic on the robot's dynamic behaviors is examined. Asadi F derived an explicit dynamic model of Delta robot by principle of virtual work [29]. The Jacobian matrices were calculated to obtain the kinematic relations in a more compact form and substituted into dynamic model.…”

Kinematics and Dynamics Analysis of a 3UPS-UPU-S Parallel Mechanism

“…V is called the pseudo-inverse of the unit velocity screw matrix S V . Through the velocity parameters from Equation (7), the displacement and acceleration can be gained by first-order numerical integration and first-order numerical differential interpolation, respectively.…”

“…However, redundantly actuated parallel mechanisms present challenges in dynamic modeling due to their complexity and computational requirements. Several methods have been proposed to analyze the dynamics of multi-rigid-body systems, including Lagrange equations [2,3], Newton-Euler equations [4][5][6], virtual work principles [7][8][9][10], Kane equations [11,12], and Gibbs-Appell equations [13,14]. The analysis of multi-rigid-body systems often relies on mathematical methods from classical mechanics and vector equations [7,15].…”

“…Several methods have been proposed to analyze the dynamics of multi-rigid-body systems, including Lagrange equations [2,3], Newton-Euler equations [4][5][6], virtual work principles [7][8][9][10], Kane equations [11,12], and Gibbs-Appell equations [13,14]. The analysis of multi-rigid-body systems often relies on mathematical methods from classical mechanics and vector equations [7,15]. Additionally, the screw theory has been extensively used for dynamic analysis, providing efficient modeling of mechanisms based on kinematic formulations through screw theory [16][17][18].…”

Dynamic Analysis of a Delta Parallel Robot with Flexible Links and Joint Clearances

“…Other approaches to dynamic DPR modeling are presented in [10], for example, the Lagrange equations, Newton-Euler formulation and the Principle of Virtual Work. An analysis of an analytical dynamic model of the Delta robot was presented in [11] and another analytical model was validated by experimental data [12]. Different methods for dynamic modeling of parallel robots are presented in [13][14][15][16][17], with numerical simulation and experimental validation.…”