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Optimum Balancing of the Four-Bar Linkage Using Fully Cartesian Coordinates

2019 , Acevedo, Mario , Orvañanos-Guerrero, María T. , Velázquez, Ramiro , Haro-Sandoval, Eduardo

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Optimización del balanceo de un mecanismo plano mediante redistribución de masas

2022 , Orvañanos-Guerrero, María T. , Acevedo, Mario , Sánchez-Gómez, Claudia , Juan Cisneros-Barba , Miguel Carrasco , Velázquez, Ramiro

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Design and Characterization of a Miniature Bio-Inspired Mobile Robot

2021 , Velázquez, Ramiro , Claudia L. Garzon-Castro , Acevedo, Mario , Orvañanos-Guerrero, María T. , Amir A. Ghavifekr

This paper presents the design, implementation, and characterization of a miniature crab-like walking robot. The first prototype developed is a four-legged servomotor actuated machine that exhibits compact dimensions, low mass, and is capable of overcoming obstacles and moving on irregular terrain and confined spaces. Its bio-inspired design ensures the compliance of its locomotion mechanism even in the presence of external disturbances. The mechanical design, the implementation of the prototype, and its electronic control approach are first discussed. Next, a kinematic analysis characterizing its motion is presented. The aim of this device is to serve as an educational supporting platform for understanding robot kinematics and legged locomotion.

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Gradient Descent-Based Optimization Method of a Four-Bar Mechanism Using Fully Cartesian Coordinates

2019 , Orvañanos-Guerrero, María T. , Sánchez-Gómez, Claudia , Mariano Rivera , Acevedo, Mario , Velázquez, Ramiro

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.

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An Alternative Method for Shaking Force Balancing of the 3RRR PPM through Acceleration Control of the Center of Mass

2020 , Acevedo, Mario , Orvañanos-Guerrero, María T. , Velázquez, Ramiro , Vigen Arakelian

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.

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A forgotten and unforgettable story. Carranza, Constitution and Catholic Church in Mexico (1914-1919)

2022 , Velázquez, Ramiro , Acevedo, Mario , Sánchez-Gómez, Claudia , Orvañanos-Guerrero, María T.

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Efficient Balancing Optimization of a Simplified Slider-Crank Mechanism

2020 , Orvañanos-Guerrero, María T. , Acevedo, Mario , Nicola Ivan Giannoccaro , Paolo Visconti , Sánchez-Gómez, Claudia , Velázquez, Ramiro

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Using Fully Cartesian Coordinates to Calculate the Support Reactions of Multi-Scale Mechanisms

2018 , Orvañanos-Guerrero, María T. , Sánchez-Gómez, Claudia , Dávalos Orozco, Oscar , Mariano Rivera , Velázquez, Ramiro , Acevedo, Mario

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Shaking Moment Balancing of a Four-Bar Mechanism Using Actuation Redundancy

2019 , Acevedo, Mario , Orvañanos-Guerrero, María T. , Velázquez, Ramiro

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Complete Balancing of the Six-Bar Mechanism Using Fully Cartesian Coordinates and Multiobjective Differential Evolution Optimization

2022 , Orvañanos-Guerrero, María T. , Acevedo, Mario , Daniel U. Campos-Delgado , Sánchez-Gómez, Claudia , Amir Aminzadeh Ghavifekr , Paolo Visconti , Velázquez, Ramiro

The high-speed operation of unbalanced machines may cause vibrations that lead to noise, wear, and fatigue that will eventually limit their efficiency and operating life. To restrain such vibrations, a complete balancing must be performed. This paper presents the complete balancing optimization of a six-bar mechanism with the use of counterweights. A novel method based on fully Cartesian coordinates (FCC) is proposed to represent such a balanced mechanism. A multiobjective optimization problem was solved using the Differential Evolution (DE) algorithm to minimize the shaking force (ShF) and the shaking moment (ShM) and thus balance the system. The Pareto front is used to determine the best solutions according to three optimization criteria: only the ShF, only the ShM, and both the ShF and ShM. The dimensions of the counterweights are further fine-tuned with an analysis of their partial derivatives, volumes, and area–thickness relations. Numerical results show that the ShF and ShM can be reduced by 76.82% and 77.21%, respectively, when importance is given to either of them and by 45.69% and 46.81%, respectively, when equal importance is given to both. A comparison of these results with others previously reported in the literature shows that the use of FCC in conjunction with DE is a suitable methodology for the complete balancing of mechanisms.