Synthesis method for linkages with center of mass at invariant link point — Pantograph based mechanisms

Wijk, Volkert van der; Herder, Just L.

doi:10.1016/j.mechmachtheory.2011.09.007

Cited by 25 publications

(49 citation statements)

References 17 publications

(27 reference statements)

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“…6, the specific kinematic conditions here imply the parallel motions of the links. For planar linkages parallel motion of links was shown to be key to find advantageous balance solutions [8,10,19]. This is since parallelograms are the basis of pantographs which are excellent mechanisms for balancing because of their properties of similarity.…”

Section: Force Balance Solutions For Specific Kine-matic and Geometrimentioning

confidence: 99%

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Force Balance of a Spatial Metamorphic 6R Closed-Chain Linkage With Specific Kinematic Conditions

Wijk

Zhang

Dai

2016

Volume 5B: 40th Mechanisms and Robotics Conference

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INTRODUCTIONDeployable, reconfigurable, and metamorphic linkages are useful for devices that need large flexibility and adaptability. For instance deployable structures are used in car roofs [1], in architecture [2], and in portable emergency shelters [3] where they need to be capable of being closed in a compact space and to extend over a large space when undeployed. Reconfigurable and metamorphic robot manipulators are capable of changing certain kinematic properties [4,5] by which they are more flexible in carrying out different tasks or they are capable to perform more complicated tasks [6,7].One challenge in the design of deployable, reconfigurable, and metamorphic linkages is to bear the forces due to the mass and the motion of the mass of the elements, which can be significant already for small dimensions. Because of gravity these linkages may collapse if not properly and continuously actuated, which can happen especially at the instant moment of mobility change when moving from one configuration mode to another. For the linkage in motion the inertial forces can cause unwanted behavior such as base vibrations, especially at high speeds. Force balance then becomes an important aspect in the design of the linkage.A force balanced linkage is designed such that the common center of mass (CoM) of all elements is in a stationary point in

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Section: Force Balance Solutions For Specific Kine-matic and Geometrimentioning

confidence: 99%

“…9a where mass m 3 extends from A 1 such that it acts as balancing mass for all elements. This solution as seen in the plane is known as the typical force balanced pantograph [8,10,19]. When m 1 , m 2 , m 3 , l 1 , e 1 , and d 2 are given, d 3 is calculated from Eq.…”

Section: Force Balance Solution Of Spatial Modementioning

confidence: 99%

Force Balance of a Spatial Metamorphic 6R Closed-Chain Linkage With Specific Kinematic Conditions

Wijk

Zhang

Dai

2016

Volume 5B: 40th Mechanisms and Robotics Conference

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“…Practical ways to move the CoM of the system and to make it stationary have been to add a set of counterweights [2][3][4][5], to add auxiliary structures [6][7][8][9], or to modify the form of the links from the early design phase [10][11][12]. A comprehensive review of the methods with illustrative examples can be seen in Reference [13].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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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“…In [14], the balancing condition of parallel robots is obtained by expressing the position vector of the center of mass as a function of the position and orientation of the platform, and of six actuated prismatic joints. In [15], a synthesis method for linkages with the center of mass at an invariant link point is presented. In [16], the shaking force minimization of high-speed robots is done via optimal control of the acceleration of the total mass center of moving links.…”

Section: Introductionmentioning

confidence: 99%

Synthesis method for the spherical 4R mechanism with minimum center of mass acceleration

Mendoza-Trejo

Cruz-Villar

Peón-Escalante

et al. 2015

Mechanism and Machine Theory

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In the mechanisms area, minimization of the magnitude of the acceleration of the center of mass (ACoM) implies shaking force balancing. This article shows an efficient optimum synthesis method for minimum acceleration of the center of mass of a spherical 4R mechanism by using dual functions, as well as, the counterweights balancing method. Once the dual function for ACoM has been formulated, one can minimize the shaking forces from a kinematic point of view. We present the synthesis of a spherical 4R mechanism for the case of a path generation task. The synthesis process involves the optimization of two objective functions, this multiobjective problem is solved by using the weighted sum method implemented in the evolutionary algorithm known as Differential Evolution. Our results shows that the magnitude of the ACoM can be reduced about 20 times. Which for the presented synthesis, is traduced in a reduction of about 89% for the shacking forces.

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Synthesis method for linkages with center of mass at invariant link point — Pantograph based mechanisms

Cited by 25 publications

References 17 publications

Force Balance of a Spatial Metamorphic 6R Closed-Chain Linkage With Specific Kinematic Conditions

Force Balance of a Spatial Metamorphic 6R Closed-Chain Linkage With Specific Kinematic Conditions

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

Synthesis method for the spherical 4R mechanism with minimum center of mass acceleration

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