Explicit dynamics formulation of Stewart-Gough platform: A Newton-Euler approach

Abstract

Dynamic analysis of parallel manipulators plays a vital role in the design and control of such manipulators. Closed-chain kinematic structure affects the dynamics formulations by several constraints. Therefore, especially for higher degrees of freedom manipulators, manipulation of implicit and bulky dynamics formulation looses the tractability of the analysis. In this paper, a methodology and some simplification tools are introduced to achieve explicit dynamics formulation for parallel manipulators. This methodology is applied for the dynamics analysis of the most celebrated parallel manipulator, namely Stewart-Gough platform. By avoiding any recursive or component-wise derivations, the resulting dynamics formulation provides more insight for designers, and can be much easier used in any model-based control of such manipulators. In order to verify the resulting dynamics equations, Lagrange method is used to derive and compare the manipulator mass matrix. This methodology can be further used to formulate the explicit dynamics of other parallel manipulators.

Modeling and Analysis of a Multi-Degree-of-Freedom Micro-Vibration Simulator

“…The dynamic model for upper platform as a rigid body ignoring the inertia of the actuators can be derived using the Newton-Euler method [14]:…”

“…Over the past decades, numerous research results have been reported on the kinematics of the GSP and relatively fewer results on the dynamic of GSP [13]. Oftadeh et al [14] presented the explicit dynamics formulation for the GSP and utilized the Lagrange method to verify the resulting dynamics equations. Dasgupta and Mruthyunjaya [15] derived an inverse dynamic formulation by the Newton-Euler approach for the GSP, with the frictional forces occurring in the joints; meanwhile the mass of inertia of the pods was taken into consideration in their study.…”

Dynamic modeling and robust nonlinear control of a six-DOF active micro-vibration isolation manipulator with parameter uncertainties

“…Energy method begins with scalar energy expressions which use Lagrange's equations, Hamilton's canonical equations, the Gibbs equations, or the Boltzmann-Hamel equations [11]. Dynamic equations formulated via Newton-Euler method [12][13][14][15] would suffer a heavy computational burden since some constraint forces are needed to be known. But the method is relatively easier to be understood and more direct than others.…”

Closed-form dynamic formulation of spherical parallel manipulators by Gibbs-Appell method

“…Several algorithms have been proposed for dynamic formulation of multi body systems that are based on Newton-Euler, Lagrange, and Virtual-Work method. Applying these modeling tools for parallel robots is usually bulky and untractable [10]. The other strategy for dynamic formulation is Gibbs-Appell (GA).…”

“…Despite the high potential of this method in dynamic analysis of multi body systems, It has been less addressed in the field of parallel robots. Dynamic modeling of parallel manipulator has been studied by several researchers through Newton-Euler method, [8], [10]. Newton-Euler method requires force analysis of individual mechanism members, and therefore, having a closed form dynamic model for the total system needs elimination of all the internal forces, which is a prohibitive task.…”