Multi-objective reliability-based optimal synthesis of path generating four-bar mechanisms: A cooperative game theoretic approach

In this study, a novel approach based on synergy of cooperative game theory, reliability-based design optimization (RBDO) and Monte Carlo simulation (MCS) is proposed to address the reliability-based multi-objective optimal synthesis of path generating four-bar mechanisms, taking into account the influence of dimensional uncertainty on the reliability of mechanism. Tracking error ([Formula: see text]), deviation of transmission angle from 90° ([Formula: see text]) and probability of failure of Grashof constraint are defined as three performance criteria whose minimization enhance the precision, quality of motion and reliability of mechanism, respectively. To do so, three objective functions are considered, namely, precision ([Formula: see text]), quality of motion ([Formula: see text]) and reliability ([Formula: see text]); each objective function is assigned to a player. To conduct the optimization procedure, a game model is proposed, in which the cooperative game scenario is employed by defining a Nash bargaining function to model the interaction between players. In this way, the three-objective optimum design of mechanism is cast into a single-objective optimization problem. The comparisons of the obtained results using the method of this research with those reported in the literature shows a significant improvement in reliability of mechanism, whilst both precision and quality of motion in deterministic design is maintained. Particularly, the tracking error and the deviation of transmission angle from 90° of the synthesized mechanism is 0.0006 and 666.36 respectively, whilst the reliability is guaranteed since no violation of Grashof constraint occurs in the presence of 10% parameter uncertainty.

MATHEMATICAL MODEL AND AREA OF EXISTENCE OF THE FAMILY CRANKS AND MOBILE MECHANISMS WITH THE MAXIMUM TRANSMISSION ANGLE

The article examines crank-rocker mechanisms. Such mechanisms are used in transport and technological machines. The article is devoted to the search for a new family of crank-rocker mechanisms. A mathematical model of a new family of crank-rocker mechanisms is obtained. In this family, the maximum transmission angle reaches 90 when the crank angle is 75. Thus, the new family of crank-rocker mechanisms differs from the known families by the position of the mechanism in which the maximum of the transmission angle function takes place. It is shown that, with a certain ratio of link lengths, the new family corresponds to the known families KKM-5 and KKM-7. The area of existence of a new family of crank-rocker mechanisms is established. This area is bounded by the arc of the circle of the unit radius and the curve. The mentioned curve is based on a joint solution of a mathematical model of a new family of mechanisms and the famous Kolchin straight line. The dependence for the minimum transmission angle is obtained. A formula for determining the angle of the rocker arm span is proposed. A graphical interpretation of the mentioned dependencies and formulas is constructed. The scope of existence of a new family of crank-rocker mechanisms and graphical interpretations are used in determining the geometric parameters of mechanisms. These mechanisms are part of a new family of mechanisms.

Dead Center Identification of Two-Degrees-of-Freedom Planar Parallel Manipulator Using Graph Theory and Transmission Angle

Parallel manipulators are widely applied for their advantages of high stiffness, load-bearing, operation speed, and precision positioning capabilities, which are required in many industrial applications. However, dead center identification is a challenging task and fundamental problem during design stage of parallel manipulators, and becomes more intractable for two-degrees-of-freedom (DOF) complex planar parallel manipulators (PPMs) design. This paper proposes a method to identify the dead center positions of two-DOF PPMs based on graph theory and transmission angle. First, these PPMs are denoted by a set of independent loops using a topological structural analysis of the kinematic chains and structural decomposition. Then, the relationship between the mobility factor and the loop factor in the same independent loop is utilized to obtain the folded or stretched operation to form the new PPMs containing the corresponding instantaneous virtual loop. Subsequently, the dead center positions can be located since the corresponding transmission angle of the new PPMs is equal to 0 deg or 180 deg. As a result, the solved dead center positions of the two-DOF three types seven-bar, nine-bar, and 11-bar PPMs will provide guidance for the proper design of these PPMs. Finally, the Jacobian method for identifying the dead center position is then used to verify the proposed method. The proposed method is systematic and programmable and can be applied to any two-DOF PPM regardless of the number of independent loops or types of joints.

Linkage and Cam Design with MechDev Based on Non-Uniform Rational B-Splines

Several software products exist in order to support engineers during the mechanism design process. The software “Mechanism Developer” (abbr. MechDev) is one of these products. MechDev provides many functionalities concerning the kinematic and kinetostatic analysis of mechanisms based on revolute, prismatic as well as cam joints. This paper will introduce the software MechDev and will outline these functionalities. Furthermore, it will name the advantages of MechDev compared to other software products. In order to give an impression of the functionality of the software, this paper also includes a special use case. This use case describes a cam mechanism with a prismatic roller-follower. In order to optimize the transmission angle of the cam mechanism, the cam is actuated by a servo drive. To mathematically model the angular input of the servo drive, Non-Uniform Rational B-Splines (NURBS) are described and applied. Thus, a nearly arbitrary input function can be described by few parameters.

3D Radiation Pattern Reconfigurable Phased Array for Transmission Angle Sensing in 5G Mobile Communication

This paper proposes a 3D radiation pattern reconfigurable antenna (RPRA) and a reconfigurable phased array (RPA) for 5G mobile communication. The antenna and array are working at 28 GHz, which is selected as a 5G communication band in many countries. The proposed phased array will be applied as sensors to find out the optimal transmitting–receiving angle in a randomly changed cellular wireless scenarios. The RPRA and RPA are fed by Substrate Integrated Waveguide (SIW) and have three switchable radiation modes: Broadside 1, Broadside 2 and Endfire. The three modes correspond to three different radiation patterns and each of them covers a different area in the Azimuth plane. An eight-element phased array constructed by the proposed RPRA, which is able to switch beam in Azimuth plane and scan in the Elevation plane, is also presented in this paper. The proposed RPA is able to provide much higher spatial coverage than the conventional phased arrays and without additional feeding and phase shifting networks. The beam switching is realized by the PIN diodes. The proposed antenna and array have planer structures and require small clearance on the ground plane which makes them compatible with mobile phones. The simulations show good performance for both RPRA and RPA.