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      9  2
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    Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates
    <jats:p>Machine vibrations often occur due to dynamic unbalance inducing wear, fatigue, and noise that limit the potential of many machines. Dynamic balancing is a main concern in mechanism and machine theory as it allows designers to limit the transmission of vibrations to the frames and base of machines. This work introduces a novel method for representing a four-bar mechanism with the use of Fully Cartesian coordinates and a simple definition of the shaking force (ShF) and the shaking moment (ShM) equations. A simplified version of Projected Gradient Descent is used to minimize the ShF and ShM functions with the aim of balancing the system. The multi-objective optimization problem was solved using a linear combination of the objectives. A comprehensive analysis of the partial derivatives, volumes, and relations between area and thickness of the counterweights is used to define whether the allowed optimization boundaries should be changed in case the mechanical conditions of the mechanism permit it. A comparison between Pareto fronts is used to determine the impact that each counterweight has on the mechanism’s balancing. In this way, it is possible to determine which counterweights can be eliminated according to the importance of the static balance (ShF), dynamic balance (ShM), or both. The results of this methodology when using three counterweights reduces the ShF and ShM by 99.70% and 28.69%, respectively when importance is given to the static balancing and by 83.99% and 8.47%, respectively, when importance is focused on dynamic balancing. Even when further reducing the number of counterweights, the ShF and ShM can be decreased satisfactorily.</jats:p>
    Scopus© Citations 11  14  2
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    An Alternative Method for Shaking Force Balancing of the 3RRR PPM through Acceleration Control of the Center of Mass
    <jats:p>The problem of shaking force balancing of robotic manipulators, which allows the elimination or substantial reduction of the variable force transmitted to the fixed frame, has been traditionally solved by optimal mass redistribution of the moving links. The resulting configurations have been achieved by adding counterweights, by adding auxiliary structures or, by modifying the form of the links from the early design phase. This leads to an increase in the mass of the elements of the mechanism, which in turn leads to an increment of the torque transmitted to the base (the shaking moment) and of the driving torque. Thus, a balancing method that avoids the increment in mass is very desirable. In this article, the reduction of the shaking force of robotic manipulators is proposed by the optimal trajectory planning of the common center of mass of the system, which is carried out by “bang-bang” profile. This allows a considerable reduction in shaking forces without requiring counterweights, additional structures, or changes in form. The method, already presented in the literature, is resumed in this case using a direct and easy to automate modeling technique based on fully Cartesian coordinates. This permits to express the common center of mass, the shaking force, and the shaking moment of the manipulator as simple analytic expressions. The suggested modeling procedure and balancing technique are illustrated through the balancing of the 3RRR planar parallel manipulator (PPM). Results from computer simulations are reported.</jats:p>
    Scopus© Citations 9  11  1
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    Balancing Conditions of the RSS’R, Spatial Mechanism
    Dynamic balancing of rigid body linkages with constant mass links is a traditional but still very active research area in mechanical engineering. It has some difficulties but the initial one is to derive the so-called balancing conditions, that are helpful to obtain different configurations for the balanced mechanism. The objective of this work is to illustrate the application of a general method to find the force and moment balancing conditions of planar and spatial linkages. It is applied for the dynamic balancing of the RSS’R spatial mechanism. The method is based on the use of Natural Coordinates so the whole system is represented only by a set of basic points, avoiding the use of angular coordinates. This facilitates obtaining the expressions for the linear momentum and for the angular momentum required to extract the shaking force and the shaking moment balancing conditions for the linkage. These conditions are interpreted and used to propose different design alternatives which can lead to a convenient design. © 2018, Springer International Publishing AG.
    Scopus© Citations 1  27  1
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    Dynamic Balancing Conditions of Planar Parallel Manipulators
    (2015) ;
    Reyes, José María
    Force and moment balancing (dynamic balancing) of rigid body linkages with constant mass links is a traditional but still very active area of research in machine dynamics and robotics. The shaking force and the shaking moment caused by all moving links can be reduced in different ways but all having a common difficulty named to derive the so-called balancing conditions, that in general can be cumbersome. In this article a novel method to find the dynamic balancing conditions based on the use of Natural Coordinates is introduced. The method is direct, efficient, and easy to automate through the application of a computer algebra system. It can be used to obtain the shaking force and the shaking moment balancing conditions for planar and spatial mechanisms.
      4  2
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    Multibody dynamics for human-like locomotion
    Multibody dynamics has been a fundamental tool for modeling, simulation and design of human-like locomotion systems. Either in the prosthetic and orthotics sector to develop devices for improvement or restoration of mobility, or as in the simulation, design, and optimization of humanoid robots. A lot of research and development has been done in these challenging areas where new mechanisms and improvements in dynamics are always welcome. The dynamic balancing of mechanisms (force and moment balancing at the fixed base) is an area that, along with multibody dynamics, can help to improve the design of human-like locomotion systems. In this chapter, the application of a force-balanced mechanism is proposed as a leg to be part of a biped robot. Stability is analyzed through the application of learning approaches based on an artificial intelligence, namely artificial hydrocarbon networks. Modeling and results from multibody dynamics simulation are presented. © 2020 Elsevier Inc. All rights reserved.
    Scopus© Citations 1  19  1