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This book covers the state-of-the-art technologies in dynamic balancing of mechanisms with minimum increase of mass and inertia. The synthesis of parallel robots based on the Decomposition and Integration concept is also covered in detail. The latest advances are described, including different balancing principles, design of reactionless mechanisms with minimum increase of mass and inertia, and synthesizing parallel robots. This is an ideal book for mechanical engineering students and researchers who are interested in the dynamic balancing of mechanisms and synthesizing of parallel robots.

This book also:

· Broadens reader understanding of the synthesis of parallel robots based on the Decomposition and Integration concept

· Reinforces basic principles with detailed coverage of different balancing principles, including input torque balancing mechanisms

· Reviews exhaustively the key recent research into the design of reactionless mechanisms with minimum increase of mass and inertia, such as the design of reactionless mechanisms with auxiliary parallelograms, the design of reactionless mechanisms with flywheels, and the design of reactionless mechanisms by symmetrical structure design.



Chapter 1. Review of Recent Advances on Reactionless Mechanisms and Parallel Robots

When parallel mechanisms are in motions, because the center of mass (CoM) is not fixed and angular momentum is not constant, vibration is often produced in the system. Shaking force and shaking moment balancing can usually be realized by making the CoM of mechanism fixed and angular momentum constant. There are generally two main ways for shaking force balancing and shaking moment balancing, balancing before kinematic synthesis and balancing at the end of the design process. For the balancing at the end of the design process, addition of counterweights and counter-rotations, addition of active dynamic balancing unit, and addition of auxiliary links are mostly used methods. The advances and problems on dynamic balancing of mechanisms are discussed in detail under the above two main categories here, and balancing through reconfiguration method is proposed, which can reduce the addition of mass and inertia. Fisher’s method belongs to the method of balancing before kinematic synthesis.
Dan Zhang, Bin Wei

Chapter 2. Design of Reactionless Mechanisms Without Counter-rotations

This chapter presents methods and principles used for balancing of planar mechanisms without counter-rotations. The fundamentals of balancing are described at first. Balancing only by counterweights provides only the force balance of mechanisms. Several basic methods which balance linkages by internal mass redistribution or adding of counterweights are introduced. These methods are the principal vector method, linearly independent vector method, complex mass method, and linear momentum method. The principles of these methods are explained in the example of the four-bar linkage and some extensions and important outcomes of these methods are added.
Vlastimil Votrubec

Chapter 3. Design of Reactionless Linkages and Robots Equipped with Balancing Assur Groups

In the present chapter, we consider the shaking moment and shaking force balancing through the use of additional Assur groups mounted on the mechanism to be balanced. Two types of mechanisms are considered: (1) the in-line four-bar linkage and (2) the planar parallel robots with prismatic pairs. For both types of mechanisms, the proposed solution allows the reduction (or even the cancellation in the case of the four-bar linkage) of the number of counter-rotations used for obtaining the shaking moment balancing, which decreases the design complexity and the inherent problems due to the use of counter-rotations (backlash, noise, vibrations, etc.). All theoretical developments are validated via simulations carried out using ADAMS software. The simulations show that the obtained mechanisms (both in-line four-bar linkages and planar parallel robots) transmit no inertia loads to their surroundings, i.e. the sum of all ground bearing forces and their moments are eliminated.
Sébastien Briot, Vigen Arakelian

Chapter 4. Design of Reactionless Planar Parallel Manipulators with Inertia Flywheel or with Base-Mounted Counter-rotations

This chapter discusses the development of reactionless planar parallel manipulators, which apply no reaction forces or moments to the mounting base during motion. Design equations and techniques are proposed which allow for the dynamic substitution of the mass of the moving platform of a parallel manipulator by three concentrated masses. The dynamic model of the moving platform consequently represents a weightless link with three concentrated masses. This allows for the transformation of the problem of the design of a reactionless manipulator into a problem of balancing pivoted legs carrying concentrated masses. The total angular momentum of the manipulator can be reduced to zero using two approaches: (1) on the basis of counter-rotations, and (2) using an inertia flywheel rotating with a prescribed angular velocity. The suggested solutions are illustrated through 3-DOF 3-RRR planar parallel manipulators. Computer simulations and the results verified by showing that the manipulator are indeed reactionless, there being no forces or moments transmitted to the base during motion of the moving platform.
Vigen Arakelian

Chapter 5. Design of Reactionless Mechanisms with Counter-Rotary Counter-Masses

In this chapter a new method to find the force and moment balancing conditions based on Natural Coordinates is introduced. The method is simple and can be highly automated, it is very prone to be used in combination with a system for the manipulation of symbolic expressions. These conditions can be interpreted and used for the creation of dynamic balanced linkages by design. The application of the method is demonstrated through the dynamic balancing of a simple pendulum (open-loop linkage) and a general four-bar mechanism (closed-loop linkage), particularly by the design of counter-rotary counter-masses applying optimization. The resulting designs are presented and their virtual prototypes simulated using a general multibody dynamics simulation software (ADAMS), specifying the resulting geometry (dimensions), shaking force, shaking moment, and driving torque.
Mario Acevedo

Chapter 6. Shaking Force and Shaking Moment Balancing of Six- and Eight-Bar Planar Mechanisms

This chapter presents the dynamic balancing technique for shaking force and shaking moment balancing of six- and eight-bar planar mechanisms. Shaking force is balance by the method of redistribution of mass and shaking moment by geared inertia elements. The planetary gears used to balance shaking moment of links not directly connected to the frame in earlier methods are mounted on the base of the mechanism which is constructively more efficient. The proposed method is illustrated by numerical examples and it is observed that better results are obtained than those of the previous method.
Peddinti Nehemiah

Chapter 7. Synthesizing of Parallel Robots Using Adjusting Kinematic Parameters Method

Force balancing is a very important issue in mechanism design and has only recently been introduced to the design of robotic mechanisms. In this chapter, a force balancing method called adjusting kinematic parameters (AKP) for robotic mechanisms or real-time controllable (RTC) mechanisms is proposed, as opposed to existing force balancing methods, e.g., the counterweights (CW) method. Both the working principle of the AKP method and the design equation are described in detail. A particular implementation of the AKP method for the RTC mechanisms where two pivots on a link are adjustable is presented. After that, a hybrid approach to force balancing of robotic mechanisms is proposed, and this hybrid approach is to combine AKP and counterweights (CW) approaches, called AKP+CW in short. The main motivation of the AKP+CW approach is that CW and AKP each has its own advantage and disadvantage, and thus a combined one may strengthen both. This chapter presents the force balancing principles and equations for the AKP+CW approach. Software called ADAMS is employed as a tool for the simulated experiment to verify the effectiveness of the proposed approach. The joint forces and torques are calculated for the trajectory tracking of the RTC mechanisms. The implication of the work to the balancing of mechanisms in general is that many different force balancing methods may be combined based on the hybridization principle proposed in this chapter to become a novel one. Simulation results show that the AKP method and AKP+CW method are consistently better than the CW method in terms of the reduction of the joint forces and the torques in the servomotors, and the smoothing of the fluctuation of the joint force.
P. R. Ouyang, W. J. Zhang, J. Huang

Chapter 8. Balancing of a 3-DOFs Parallel Manipulator

This chapter gives an overview on static and dynamic balancing. Basic approaches are discussed for achieving the design of mechanisms having a fully balanced behavior under different operation conditions. A formulation is proposed to address the effects of balancing on mass distributions and dynamic performance. The proposed formulation is applied for the dynamic balancing of a three DOFs (degrees-of-freedom) spatial parallel manipulator, namely CaPaMan 2bis (Cassino Parallel Manipulator 2bis). This parallel manipulator has three identical legs, where each leg is composed by a four-bar mechanism, an orthogonal revolute joint, and a spherical joint that is attached on the mobile platform. The proposed solution for achieving the balancing of CaPaMan 2bis is based on the use of counter-rotary counterweights. The obtained results are validated by simulations by using a general-purpose software for multi-body dynamics analysis.
D. Cafolla, G. Carbone, M. Ceccarelli

Chapter 9. Dynamic Balancing with Respect to a Given Trajectory

To control the parallel link robots with better performance in terms of high rigidity, high degree of accuracy, high speed or acceleration, high load-carrying capacity, static balancing, and dynamic balancing are important factors. Generally, static balancing can be obtained by using counterweights or springs, and no computer control is involved. On the other hand, dynamic balancing utilizes control system to coordinate the motions of balancing elements. In this chapter, we persist on dynamic balancing with respect to a given trajectory for the parallel link robots by modeling control system. This chapter is organized in the following manner. In section “Modeling of Kinematics,” geometric feature of Stewart Platform is introduced and modeling process of kinematics and Jacobian matrices is introduced. In section “Jacobian Analysis,” modeling process of Jacobian matrix is presented. In section “Dynamics,” modeling process of dynamics equations of a six DOF Stewart Platform is presented. In section “The Operational Space Formulation,” the Operational Space Formulation is presented to control task dynamics at the end-effector. In section “Trajectory Generation,” modeling method of smooth trajectory is presented. In section “Trajectory Tracking Control,” control method to realize stable trajectory tracking motion is presented. Finally, control method to realize dynamic balancing with respect to a given trajectory is presented in section “Dynamic Balancing with Respect to a Given Trajectory.”
Taizo Yoshikawa

Chapter 10. Dynamic Balancing and Flexible Task Execution for Dynamic Bipedal Walking Machines

Effective use of robots in unstructured environments requires that they have sufficient autonomy and agility to execute task-level commands with temporal constraints successfully. A challenging example of such a robot is a bipedal walking machine, particularly one of humanoid form. Key features of the human morphology include a variable base of support and a high center of mass. The high center of mass supports the ability to support a high “sensor package”; when standing erect, the head can see over obstacles. The variable base of support allows both for operation in tight spaces, by keeping the feet close together, and stability against disturbances, by keeping the feet further apart to widen the support base. The feet can also be placed in specific locations when there are constraints due to challenging terrain. Thus, the human morphology supports a range of capabilities, and is important for operating in unstructured environments as humans do. A bipedal robot with human morphology should be able to walk to a particular location within a particular time, while observing foot placement constraints, and avoiding a fall, if this is physically possible. This is a challenging problem because a biped is highly nonlinear and has limited actuation due to its limited base of support. This chapter describes a novel approach to solving this problem that incorporates three key components: (1) a robust controller that is able to use angular momentum to enhance controllability beyond the limits imposed by the support base; (2) a plan specification where task requirements are expressed in a qualitative form that provides for spatial and temporal execution flexibility; and (3) a task executive that compiles the plan into a form that makes the dynamic limitations explicit, and then executes the compiled form using the robust controller.
Andreas Hofmann

Chapter 11. Design of Reactionless Mechanisms Based on Constrained Optimization Procedure

This chapter presents an optimization technique to dynamically balance planar mechanisms by minimizing the shaking forces and shaking moments due to inertia-induced forces. Dynamically equivalent systems of point masses which represent rigid links and counterweights are useful for developing optimization technique. The point-mass parameters are explicitly identified as the design variables. The balancing problem is formulated as both single-objective and multi-objective optimization problem and solved using genetic algorithm which produces better results as compared to the conventional optimization algorithm. Also, for the multi-objective optimization problem, multiple optimal solutions are created as a Pareto front using the genetic algorithm. The reduction of shaking force and shaking moment is obtained by optimizing the link mass distribution and counterweight of their point masses. The inertial properties of balanced mechanism are then computed in reverse by applying dynamical equivalent conditions from the optimized design variables. The effectiveness of the methodology is shown by applying it to problems of planar four-bar, slider-crank, and Stephenson six-bar mechanisms.
Himanshu Chaudhary, Kailash Chaudhary

Chapter 12. Balancing of Planar Mechanisms Having Imperfect Joints Using Neural Network-Genetic Algorithm (NN-GA) Approach

As a result of design, manufacturing and assembly processes or a wear effect, clearances are inevitable at the joints of mechanisms. In this study, dynamic response of mechanism having revolute joints with clearance is investigated. A four-bar mechanism having two revolute joints with clearance is considered as a model mechanism. A neural network was used to model several characteristics of joint clearance. Kinematic and dynamic analyses were achieved using continuous contact mode between journal and bearing. A genetic algorithm was also used to determine the appropriate values of design variables for reducing the additional vibration effects due primarily to the joint clearance. The results show that the optimum adjusting of suitable design variables gives a certain decrease in shaking forces and their moments on the mechanism frame.
Selçuk Erkaya, İbrahim Uzmay

Chapter 13. Minimization of Shaking Force and Moment on a Four-Bar Mechanism Using Genetic Algorithm

In this study, optimal balancing of a 2D articulated mechanism is investigated to minimize the shaking force and moment fluctuations. Balancing of a four-bar mechanism is formulated as an optimization problem. On the other hand, an objective function based on the subcomponents of shaking force and moment is constituted, and design variables consisting of kinematic and dynamic parameters are defined. Genetic algorithm is used to solve the optimization problem under the appropriate constraints. By using commercial simulation software, optimized values of design variables are also tested to evaluate the effectiveness of the proposed optimization process. This work provides a practical method for reducing the shaking force and moment fluctuations. The results show that both the structure of objective function and particularly the selection of weighting factors have a crucial role to obtain the optimum values of design parameters. By adjusting the value of weighting factor according to the relative sensitivity of the related term, there is a certain decrease at the shaking force and moment fluctuations. Moreover, these arrangements also decrease the initiative of mechanism designer on choosing the values of weighting factors.
Selçuk Erkaya

Chapter 14. Optimal Balancing of the Robotic Manipulators

The balancing of robotic systems is an important issue, because it allows for significant reduction of torques. However, the literature review shows that the balancing of robotic systems is performed without considering the traveling trajectory. Although in static balancing the gravity effects on the actuators are removed, and in complete balancing the Coriolis, centripetal, gravitational, and cross-inertia terms are eliminated, it does not mean that the required torque to move the manipulator from one point to another point is minimum. In this chapter, “optimal balancing” is presented for the open-chain robotic system based on the indirect solution of open-loop optimal control problem. Indeed, optimal balancing is an optimal trajectory planning problem in which states, controls, and all the unknown parameters associated with the counterweight masses or springs must be determined simultaneously to minimize the given performance index for a predefined point-to-point task. For this purpose, on the base of the fundamental theorem of calculus of variations, the necessary conditions for optimality are derived which lead to the optimality conditions associated with the Pontryagin’s minimum principle and an additional condition associated with the constant parameters. In this chapter, after presenting the formulation of the optimal balancing and static balancing, the obtained optimality conditions are developed for a two-link manipulator in details. Finally the efficiency of the suggested approach is illustrated by simulation for a two-link manipulator and a PUMA-like robot. The obtained results show that the proposed method has dominant superiority over the previous methods such as static balancing or complete balancing.
A. Nikoobin, M. Moradi

Chapter 15. Dynamics and Control of Planar, Translational, and Spherical Parallel Manipulators

This chapter focuses on a study of the dynamics and control of planar, translational, and spherical parallel manipulators. These mechanisms are the most often used in different applications. The synthesis of these mechanisms is carried out by means of screw groups. The dynamics and control are considered by means the constraint equations. The control algorithms based on dynamical model without linearization use the concept of inverse dynamic problems.
Victor Glazunov, Sergey Kheylo

Chapter 16. Dynamic Modelling and Control of Balanced Parallel Mechanisms

Balancing is an important issue related to the design of mechanical systems in general, and also parallel mechanisms, in particular. In fact, the performance of parallel mechanisms associated with specific applications depends on the choice of the balancing method, namely, either static or dynamic, either passive or active, whether it is valid for a given trajectory or even for any motion. The main contribution of this work is to highlight the importance of the dynamic modelling process in order to achieve the compensation conditions associated with the chosen balancing technique. Due to the fact that parallel mechanisms have highly complex structures, the use of dynamic formalisms that employ redundant generalized coordinates, in association with the successive coupling of additional balancing elements to the original system model, can bring remarkable benefits. Additionally, this book chapter also discusses the impact of the dynamic model, developed in accordance with the methodology shown here, for the control strategy of parallel mechanisms. Finally, the simulation results demonstrate how effective is the presented methodology for the planar 5-bar with revolute joints (5R).
Renato Maia Matarazzo Orsino, André Garnier Coutinho, Tarcisio Antonio Hess Coelho

Chapter 17. Controlled Biped Balanced Locomotion and Climbing

This chapter describes the control principles necessary for an articulated biped model to accomplish balanced locomotion during walking and climbing. We explain the synthesizes mechanism for coordinated control of lower-body joints (i.e., ankle, hip, and knee). A humanoid biped can have a large number of degrees of freedom (DOF) that make it challenging to create physically correct, plausible and efficient motions. While we are able to define the physical principles of unintelligent models (e.g., multi-rigid body systems), the area of actively controlling a virtual character to mimic real-world creatures is an ongoing area of research. We focus on the control strategy and stability factors during continuous motion for the performing of essential rudimentary tasks (i.e., walking and climbing). We use a multi-level feedback mechanism to generated motion trajectories for the different actions, such as, stepping and walking. For example, the support leg is controlled through active forces (i.e., actuated joint feedback) based upon the control strategy to create a targeted set of parabolic trajectories for the action (e.g., stepping or climbing). The parabolic trajectories control the articulated skeleton while taking into account environmental influences (e.g., terrain height and balance information); with control parameters, such as leg-length, centre-of-mass (COM) location, and step-length being fed-back into the control mechanism.
Benjamin Kenwright

Chapter 18. Dynamic Balancing of Mobile Robots in Simulation and Real Environments

Transferring an evolved control system from a simulated environment to the physical world poses a number of challenges. One of the most challenging control tasks is to generate a stable walking gait for a bipedal robot. We describe a method using a combination of repetitive splines and genetic algorithms to evolve a simulated control system for a humanoid robot, which is subsequently transferred to a real robot hardware. Multiple dynamic simulation systems can be simultaneously employed to provide a valid range of simulation variance. This will result in a much smaller reality gap and ultimately in a more robust control algorithm for the real robot.
Adrian Boeing, Thomas Bräunl

Chapter 19. Balancing Conditions of Planar and Spatial Mechanisms in the Algebraic Form

This chapter deals with an approach to formulate balancing conditions for the shaking force and shaking moment of planar mechanisms and spatial mechanisms. In the Mechanism Theory, every Mechanism has p moving members and a non-moving frame. According to tradition, a planar 8R-eightbar mechanism is a multibody system with 7 moving bodies.
Nguyen Van Khang, Nguyen Phong Dien

Chapter 20. Static Balancing of Articulated Wheeled Vehicles by Parallelogram- and Spring-Based Compensation

Articulated wheeled vehicles (AWVs) offer superior uneven terrain traversal capabilities by virtue of the superior reconfigurability within their articulated structure. However, this capability can be realized only at the price of increased actuation-based equilibration, oftentimes solely to support the gravitational loading. Hence, the simultaneous reduction of the overall actuation remains one of the critical challenges in such AWVs.
In this chapter, we address the static balancing of six degree-of-freedom AWVs with multiple leg-wheel subsystem. Static balancing is defined as a set of conditions on dimensional and inertial parameters of articulated vehicle components which ensure that the weight of the links and platform does not produce any torque/force at the actuators for any configuration of vehicle. In this study, elastic elements such as springs are employed in conjunction with parallelogram linkages to achieve the static balancing. The underlying principle is to realize an overall articulated system whose total potential energy including the elastic potential energy stored in springs and gravitational potential energy becomes constant.
Aliakbar Alamdari, Venkat Krovi
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