Shaking Force Balancing Research Articles

Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators

In this paper, the environmental uncertainties are taken into account when designing a robotic manipulator to balance the shaking force, shaking moment, and torque. The proposed robust balancing design approach does not consider the probability distributions of the uncertainties and is addressed without dependence on specific trajectories. This is expressed as a nonlinear constrained multiobjective optimization problem in which the nominal performance in the time-independent terms of the shaking force balancing, the shaking moment balancing, and the torque delivery, as well as their three sensitivities to uncertainties, are simultaneously optimized to provide a set of link shapes that match link mass distributions in a single stage. The proposal is applied to a three-degree-of-freedom serial-parallel manipulator, and the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the associated problem. Comparative results with other design approaches reveal that the selected design achieves a suitable tradeoff in balancing the shaking force balancing, the shaking moment balancing, and the torque delivery and their sensitivities, leading to a reduction in their values and variations under mass changes in the manipulator end-effector with different operating conditions (tasks).

Dynamic balancing of mechanisms with flexible links

The dynamic balancing of flexible mechanisms, that is, the reduction or elimination of shaking forces and shaking moments on the support structure, is considered. Two approaches are pursued: one uses similarity and the other modal balancing. A single rotating link can be balanced by a properly scaled countermass, for which balancing criteria are given. If all balancing conditions are satisfied, shaking force balance can even be achieved if geometric non-linearities are taken into account. This single link can be extended to a translator. Owing to the unscaled pitch of the translator and the asymmetric driving motor, no perfect shaking force balance is achieved, but the results can be considered satisfactory. Then, the dynamic balancing of a four-bar mechanism with a flexible coupler by means of modal balancing is shown. If the coupler is supported at the nodes of the first free vibration mode, this mode can be suppressed in the shaking force and shaking moment response. By supporting the coupler at four points with two whippletree mechanisms, the contribution of the first three symmetric vibration modes can be significantly reduced.

Shaking force balancing of a 2-DOF isotropic horological oscillator

Despite centuries of research and significant advances, the escapement mechanism used to count and maintain oscillations of mechanical time bases remains a complex mechanism and a major source of energy losses. We showed in previous work that, instead of the widely used rotational one degree-of-freedom (DOF) oscillators, 2-DOF flexure oscillators have the potential of revolutionizing mechanical watchmaking by eliminating the traditional escapement, replacing it by a simple crank driving a pin. Additionally, using flexures increases the quality factor of the time base, leading to further potential improvements in timekeeping accuracy and energy consumption. However, a significant challenge of these new time bases is their balancing such that the influence of external accelerations on their frequency is minimized, a necessary condition for accurate timekeeping in portable applications. This article presents a novel 2-DOF planar flexure oscillator called Wattwins and demonstrates how it can be made insensitive to linear accelerations such as gravity. For this purpose, a new approach to shaking force balancing is developed based on the decomposition of perturbations into effects corresponding to different orders of center of mass displacement. A full analytical model for frequency tuning and shaking force balancing of the 2-DOF oscillator is derived using a pseudo-rigid-body model and assuming that it can be decomposed into two independent 1-DOF oscillators. The results are validated by the finite element method and show that practical mechanical watch specifications can theoretically be reached. A physical prototype was also constructed and preliminary experimental results confirm the theory as well as the simulations.

Balancing of the Orthoglide Taking into Account Its Varying Payload

For fast-moving robot systems, the fluctuating dynamic loads transmitted to the supporting frame can excite the base and cause noise, wear, and fatigue of mechanical components. By reducing the shaking force completely, the dynamic characteristics of the robot system can be improved. However, the complete inertial force and inertial moment balancing can only be achieved by adding extra counterweight and counter-rotation systems, which largely increase the total mass, overall size, and complexity of robots. In order to avoid these inconveniences, an approach based on the optimal motion control of the center of mass is applied for the shaking force balancing of the robot Orthoglide. The application of the “bang–bang” motion profile on the common center of mass allows a considerable reduction of the acceleration of the total mass center, which results in the reduction of the shaking force. With the proposed method, the shaking force balancing of the Orthoglide is carried out, taking into account the varying payload. Note that such a solution by purely mechanical methods is complex and practically inapplicable for industrial robots. The simulations in ADAMS software validate the efficiency of the suggested approach.

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

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.

Optimum Shaking Force Balancing of Planar 3-RRR Parallel Manipulators by means of an Adaptive Counterweight System

This paper deals with the problem of optimum balancing of planar 3-RRR parallel robots for fast manipulation. It is known that in fast robots shaking forces on the frame vary greatly during a cycle of operation. Such forces can cause vibrations having various negative impacts. Several balancing techniques have been developed to solve this problem in planar 3-RRR parallel robots. However, it is known that the manipulators after complete shaking force balancing become very heavy, which leads to the significant increase of input torques and dynamic loads in the joints. This is why in the present study an optimum shaking force balancing of planar 3-RRR parallel manipulators by means of an adaptive counterweight system is proposed.

Optimum Shaking Force Balancing of Planar 3-RRR Parallel Manipulators by means of an Adaptive Counterweight System

Optimum Shaking Force Balancing of Planar 3-RRR Parallel Manipulators by means of an Adaptive Counterweight System

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

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 show that the magnitude of the ACoM can be reduced by about 20 times, which for the presented synthesis, is traduced to a reduction of about 89% for the shaking forces.

Critical review on complete dynamic balancing of mechanisms and parallel robots

When mechanisms and parallel manipulators move, due to the fact that the centre of mass is not fixed and angular momentum is not constant, they often produce vibrations in the base. Shaking force balancing can be achieved by making the centre of mass of mechanism be fixed, i.e. linear momentum is constant; shaking moment balancing can be achieved by making the angular momentum constant. There are generally two main ways for shaking force balancing and shaking moment balancing, i.e. 'balancing before kinematic synthesis' and 'balancing at the end of the design process'. Under the category of balancing at the end of design process, add counterweights and counter-rotations, add ADBU and add auxiliary links are mostly used principles; here a new method is proposed, i.e. balancing through reconfiguration, which can reduce the addition of mass and inertia. Fisher's method belongs to the method of balancing before kinematic synthesis. In this paper, we will discuss the advances and problems on dynamic balancing of mechanisms in detail under the above two main categories. Two main contributions of the paper can be concluded as follows: new reactionless parallel manipulators are derived and dynamic balancing through reconfiguration concept is proposed in first time.

Estimation of Counterweight for Shaking Force Balancing of a Crank-Rocker Mechanism

This paper proposes a method of balancing the shaking force of a crank-rocker mechanism which rotates at a constant angular speed with zero-unbalanced angle. In this approach, the kinematic synthesis and dynamic behavior of the mechanism are combined. The method is realized by modeling the mass of the connecting rod to represent two concentrated masses placed at the crank and rocker pins. The shaking forces balancing are done by adding counterweight masses to the crank and the rocker. The verification and numerical computation of the proposed balancing technique were carried out using ADAMS Software. The results showed that the sum of all the resultant forces was completely eliminated for the newly-balanced crank rocker mechanism.

Partial dynamic balancing of a 6-DOF haptic device

This article presents the partial dynamic balancing of a 6-DOF (degree of freedom) haptic device. At first, the motion of the 3-DOF rotational part is decoupled with the motion of the 3-DOF translational part, because the former has no effect on the baseplate, so it can be considered as a whole and only discusses the 3-DOF translational part in the process of calculating dynamic balancing. The main feature of this mechanism is that the system is symmetric about the Cartesian coordinate, so the dynamic balancing of the 3-DOF translational part can be simplified to the dynamic balancing of 1-DOF translational part. The conditions of shaking force balancing can be obtained by keeping the linear momentum constant, and the conditions of shaking moment balancing can be get by minimizing the rate of the angular momentum. Finally, simulation examples are given to verify that the centre of mass of the partial dynamically balanced mechanism is fixed, and the global reaction forces on the baseplate are zero, and the global reaction moments on the baseplate decrease about five times at all times and for arbitrary trajectories.

Shaking force minimization of high-speed robots via centre of mass acceleration control

This paper deals with the problem of shaking force balancing of high-speed manipulators. The known solutions of this problem are carried out by an optimal redistribution of moving masses which allows the cancellation or the reduction of the variable loads on the manipulator frame. In this paper an innovative solution is developed which is based on the optimal control of the robot links centre of masses. Such a solution allows the reduction of the acceleration of the total mass centre of moving links and, consequently, the considerable reduction in the shaking forces. The efficiency of the suggested method is illustrated by the numerical simulations carried out for different trajectories: for examined planar two and three link serial manipulators the shaking force reduction reaches up to 77%. This approach is also a more appealing alternative to conventional balancing methods because it allows the reduction of the shaking force without counterweights. As a result, the input torques are also decreased, which is shown using dynamic simulation software.

Generalized Lanchester balancer

The Lanchester balancer consists of equal counter rotating weights sized and aligned to eliminate the frequency terms of the frame shaking force. This approach of harmonic balancing is well known in engine design. It is one of the more preferment balancing techniques, which allows the reduction of vibrations in high-speed mechanical systems with reciprocating motion. However, the Lanchester balancer is only used for the balancing of axial slider–crank mechanisms (i.e. mechanism without eccentricity, when the sliding axis passes through the fixed pivot of the input crank). The same problem concerning off-set crank–slider mechanisms has not been considered. In this paper, for the first time, the generalized Lanchester balancer is proposed, which allows the shaking force balancing of crank–slider mechanisms of large eccentricity. As in the case of classical Lanchester device, the balancing is carried out by counter rotating weights. However, in this case, the dispositions of weights are determined by taking into account the eccentricity of slider guide. Numerical simulations carried out using the software ADAMS illustrate the proposed balancer.

Optimum dynamic balancing of planar parallel manipulators based on sensitivity analysis

This paper addresses the optimum dynamic balancing of planar parallel manipulators exemplified with a 2 DOF parallel manipulator articulated with revolute joints. The dynamic balancing is formulated as an optimisation problem such that while the shaking force balancing is accomplished through analytically obtained balancing constraints, an objective function based on the sensitivity analysis of shaking moment with respect to the position, velocity and acceleration of the links is used to minimise the shaking moment. Sets of optimisation results corresponding to various combinations of the elements of the objective function are evaluated in order to quantify their influence on the resulting shaking moment, ground forces and the driving torques. The results prove that the proposed optimisation approach can be used to completely eliminate the shaking force and to minimise the shaking moment transmitted to the frame of the parallel mechanism. For parallel manipulators or mechanisms with higher degrees of freedom, for which it is virtually impossible to obtain shaking force balancing conditions analytically, we propose an alternative constrained optimisation procedure. This procedure is based on the fact that while the magnitude of either the shaking force or the shaking moment can be bounded through including a set of constraints in the optimisation algorithm, the sensitivities of the other, either those of the shaking force or the shaking moment, can be minimised.

Improving motion tracking of servomotor-driven closed-loop mechanisms using mass-redistribution

This paper proposes a new design methodology for the improvement of motion tracking performance of single-freedom closed-loop mechanisms (actuated by controlled servomotors) under the operation conditions of robot manipulators. In particular, this design methodology suggests a mass redistribution scheme (prior to designing controllers), which follows the principle of a full shaking force balancing scheme, for the modification of an existing mechanism, with the aim to obtain a “simple” system dynamic model and thus to facilitate controller design. By taking a four-bar mechanism as example, the paper will show that motion-tracking performance of the mechanism is significantly improved by simply applying a conventional proportional-plus-derivative control algorithm. Simulation studies on cases of velocity tracking and trajectory tracking verify the effectiveness of the proposed methodology.

Optimum Balancing of Shaking Force and Shaking Moment for Spatial RSSR Mechanism Using Genetic Algorithm.

In this paper, we propose a new method, the comprehensive mass distribution method, for an optimum balancing of the shaking force and shaking moment of spatial RSSR mechanism (a spatial four-bar mechanism with two Revolute and two Spherical joints). The method consists of two parts:(1) optimizing the mass distribution of the link itself, and (2) adding weights to the end of the link. A genetic algorithm as an optimization technique is used in this study. Some examples are given, and the results show that the balancing effectiveness of the new method is better than that achieved by the conventional method and the weight of the mechanism is decreased. The shapes of optimized links are obtained using the small element superposing method.

An enzymatic immunoassay for insulin-like growth factor-I (IGF-I)

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 show that the magnitude of the ACoM can be reduced by about 20 times, which for the presented synthesis, is traduced to a reduction of about 89% for the shaking forces.

Comparison of three immunoassay kits for serum thyroglobulin

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 show that the magnitude of the ACoM can be reduced by about 20 times, which for the presented synthesis, is traduced to a reduction of about 89% for the shaking forces.

Immunoenzymatic assay of insulin-like growth factor binding protein-3

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 show that the magnitude of the ACoM can be reduced by about 20 times, which for the presented synthesis, is traduced to a reduction of about 89% for the shaking forces.

Optimum balancing of a class of multiloop linkages by function cognate transformations

The paper deals with the well-known class of complex mechanisms which remain kinematically invariant (function cognates) w.r.t. the angular rearrangement of their sub-linkages, and reveals the potentials of these transformations for optimum balancing of such mechanisms. Providing complete shaking force balancing, two general problems are specifically discussed: (a) minimization of the total balancing mass, and (b) shaking moment minimization. An essentially general analysis provides all basic results in explicit form, proves the existence of conjugate solutions correspondent to equal balancing masses, and establishes nontrivial situations when certain counterweights are completely canceled. A series of examples illustrate the theory, its merits and limitations.