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Walking and Working Surfaces
Published in W. David Yates, Safety Professional’s Reference and Study Guide, 2020
In this section, it is understood that the calculations and equations used are for free falling objects only. They do not apply when an object or body is under additional power or force, other than gravity. When calculating the rate of a fall, there are four basic equations that can be used. Collectively, these equations are referred to as the “kinematic equations”. The kinematic equations are used to calculate, the displacement, velocity, time, and/or acceleration of an object or body. d=vit+12at2vf=vi+atvf2=vi2+2add=vi+vf2t
Multi-objective genetic algorithm and Castigliano’s theorem for stiffness optimisation of parallel robots: case study of conventional Stewart platforms
Published in Australian Journal of Mechanical Engineering, 2023
Hadi Kalani, Amir Rezaei, Naser Mostashiri
The proposed methodology is shown in Figure 1. First, the inverse kinematics of the considered robot is studied. This helps in relating the value of the joint coordinates corresponding to the end-effector configuration. Moreover, the kinematics equations can be used in extracting stiffness equations of the robot. Then, in the dimensional optimisation problem, it is essential to focus on the various constraints treated in a problem of the robot dimensions. Next, the stiffness of the parallel robot in its workspace is obtained. This value depends on geometry, the topology of the robot’s structure, and the position and orientation of the end-effector within its workspace. The stiffness of the actual robotic manipulator is obtained by employing Castigliano’s theorem and strain energy.
An inverse dynamics based fuzzy adaptive state-feedback controller for a nonlinear 3DOF manipulator
Published in International Journal of Modelling and Simulation, 2023
M. J. Mahmoodabadi, N. Nejadkourki
In this research, a new fuzzy adaptive state-feedback controller based on the inverse dynamics was introduced to control the joint positions of a nonlinear 3D RPP robot manipulator. At first, via derivation of the forward kinematics equations of the robot, its workspace was investigated. Then, its dynamical equations were found by the LaGrange method, and a state-feedback controller was designed by employing the inverse dynamic scheme. Further, the gradient descent method and sliding mode surfaces were utilized to adapt the control gains over time. Besides, a fuzzy system was designed based on the singleton fuzzifier, center average defuzzifier and Mamdani product inference engine to improve the performance of the controller. Simulation results indicated that the proposed strategy has some advantages such as shorter settling time and more robustness, when those were compared to the results of the controllers introduced in literature. Eventually, the following future works are proposed to continue this work. Utilizing the introduced fuzzy adaptive state-feedback controller for other nonlinear dynamics having structural or unstructural uncertainties.Optimizing the constant control parameters using evolutionary algorithms.Implementing the suggested approach on real systems to evaluate the related experimental results.
A unique robust controller for tracking and stabilisation of non-holonomic vehicles
Published in International Journal of Control, 2020
Mohamed Maghenem, Antonio Loría, Elena Panteley
In these new coordinates, the error kinematics equations become The complete system also includes Equation (2).