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Mechanisms form part of many different production machines, e.g. weaving machines, printing machines or packaging machines. The energy-efficiency of their built-in mechanisms is crucial for the profitability of these machines. In many cases a considerable part of the energy to drive the mechanisms has to be applied to accelerate and decelerate link...
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... structure of the mechanism as well as the nomenclature is shown in Fig. 2. The contemplated Watt-II-Mechanism is a plane, sequential arrangement of two fourbar mechanisms. The mechanism is composed of a crank-rocker-mechanism A 0 -A-B-B 0 and a rocker-slider-mechanism B 0 -C-D as shown in Fig. ...
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... structure of the mechanism as well as the nomenclature is shown in Fig. 2. The contemplated Watt-II-Mechanism is a plane, sequential arrangement of two fourbar mechanisms. The mechanism is composed of a crank-rocker-mechanism A 0 -A-B-B 0 and a rocker-slider-mechanism B 0 -C-D as shown in Fig. ...
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... index numbers of the parameters indicate the corresponding links according to Fig. 2. The length l 3B is the length between the joints B 0 and B, l 3C denotes the length between the joints B 0 and C. The coordinates of the centers of gravity of the links are indicated in local, body-fixed coordinate systems. Due to the fact, that the mechanism is a plane mechanism, only the J zz components of the mass mo- ment of ...
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... optimization problem is formulated as a constrained optimization problem. In order to achieve a workable mechanism, the chain A 0 -A-B-B 0 according to Fig. 2 has to fulfill the Grashof condition. The chain B 0 -C-D has to be closable. Upper and lower limits (boundaries) of the design parameters, so-called box constraints, have to be set. Apart of these constraints, further constraints can be ...
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Citations
... A meansquare root of the sum squared discrete values of all reaction forces in the manipulator was adopted as the objective function in [24]. The average force was minimized to design the statically balanced mechanism in [25]. Schwarzfischer [26] minimized the difference of the output motion compared to the desired output motion to design energy-efficient six-bar Watt-II-Mechanism. ...
This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.
... This procedure merges kinematic and dynamic-force considerations as shake moments and forces, input torque variation and bearing reactions. An energy efficient dynamic synthesis method for crank-slider path generator mechanisms is proposed in [18] by driving the mechanisms in their Eigenmotion. There, the link lengths are obtained by minimizing the error in the generated path. ...
... To minimize the maximal Joint-Force given a task, it is necessary to find the angle , for a specific mechanism, in one cycle, where this force is maximum. Thus, the optimization problem is written (18) To solve the minimization problem, the derivatives of with respect to (designated as ) are required (19) where (20) ...
Dynamic Joint-Forces in a mechanism produce vibration and wear, decreasing its life span. Many studies have been carried out on optimization of mechanisms dynamic behaviour; however, few of it are focused on the reduction of Joint-Forces. Therefore, this work presents a method to obtain the link lengths of Function Generation Four-Bar Linkages, minimizing the maximum dynamic force in the joints. The study assumes that the crank rotates with constant angular velocity and the rocker moves a high amount of inertia between two positions. Hence, the mechanism mass and inertia is considered negligible. The equations of motion are set up together with Dead-Center Construction method after Alt. To analyze the behaviour of the Joint-Forces, all the equations are parametrized, finding out that the maximum Joint-Force is minimizable for every task given. The minimization of the Joint-Forces is achieved by using simple algorithms as Bisection and Regula-Falsi Illinois. The results show that this method reduces the maximal Joint-Force by a mean value of 8.5%, with respect to the Dead-Center Construction method with Transmission Angle Minimization. Moreover, for some tasks, the force reduction could reach up to 60%. Furthermore, this method solves the problem of null-length crank and rocker for centric crank-rocker mechanisms, generated by the Transmission Angle minimization.
... Hereby, both kinematic and mass parameters have to be adjusted simultaneously. The presented procedure was already utilised by the authors in order to synthesise a slider-crank-mechanism (Schwarzfischer et al., 2017) and a Watt-II-mechanism (Schwarzfischer et al., 2018). Within this chapter, the complete procedure is presented in detail in a structured way. ...
... The presented method is applicable for all transmission linkages with mobility M = 1. An example of the use of the method in order to synthesise a crank-slider mechanism was given in Schwarzfischer et al. (2017). Good results could be obtained also by using the method in order to synthesise a crank-rocker mechanism. ...
... The general calculation steps within the objective function in the case of negligible potential energy of the system calculate the input angular velocity in Eigenmotion for and a fixed initial angular velocity integrate numerically in order to derive calculate the output Eigenmotion:calculate the normalized output Eigenmotion and the normalized desired motion both for compare the normalized output Eigenmotion to the normalized desired motion Source:Schwarzfischer et al. (2017) ...
To counter rising energy prices and increasing global energy consumption, a long-term approach to sustainability is to improve production through efficient process design. Operation in the so-called Eigenmotion is an approach from machine dynamics with which mechanisms can be operated in an energy-efficient and material-saving way. Servo drives are used to generate the complex, periodic trace of the Eigenmotion. This approach is already established in mechanisms consisting of planar linkages. However, there is still no transfer of this principle to cam mechanisms conducted at IGMR. As so-called dwell mechanisms, cam mechanisms are used in numerous highly dynamic machines. This paper presents the development of an energy-efficient dwell mechanism based on a cam mechanism utilizing the Eigenmotion.
The paper presents concept of energy efficient motion control of robots and other machines based on structures with tensegrity features and/or cable-driven mechanisms. The essence of concept is generalization of so called eigenmotion idea for these multi-DOF complex mechanisms. The term eigenmotion here refers to a motion of a mechanism in which the constant sum of kinetic and potential energy is maximally preserved. The operation of the drives is ideally used only to eliminate passive resistances and to minimize deviations of motion from the required trajectory. The main advantage of mechanisms with tensegrity features and cable-driven ones is a relatively high number of elements such as springs, active cables or variable bodies, whose energy absorbing properties can be suitably adjusted during design and some also continuously during operation. The variability of attainable eigenmotion trajectories of these types of mechanisms can be further extended thanks to number of drives higher than number of end-effector degrees of freedom. The concept is demonstrated on two planar systems, one structure with tensegrity features and one serial–parallel cable-driven robot. The examples show the optimization of the parameters to achieve the eigenmotion properties on the given trajectories, as well as the change of the eigenmotion trajectory by changing the adjustable parameters. The final control of mechanical models along energy efficient trajectories is realized by computed torque control method.
Much research have been carried out to synthesize linkages, yet a few is concentrated on the dynamic behavior of six bar linkages in the early stages of the design process. Therefore, we present a two-step synthesis method for function generator six-bar linkages that includes constraints related to the dynamic behavior of the mechanism. The first stage focuses on matching eight given precision positions and the second stage on minimizing the reaction forces. Both minimization problems are solved with a genetic algorithm in MATLAB™. The results are compared with a multi-body simulation in MSC ADAMS™.
