A Kinematical Analysis of the Flap and Wing Mechanism of a Light Sport Aircraft Using Topological Models

In this, paper, we propose a method of kinematic analysis of a planar mechanism with application to the flap and wing mechanism of a light sport aircraft. A topological model is used to describe a mechanical system, which is a model that allows the study of the maneuverability of the system. The proposed algorithm is applied to determine the velocity and acceleration field of this multibody mechanical system. The graph associated with the mechanical system is generated in a new formulation and based on it, the fundamental loops of the graph are identified (corresponding to the independent loops of the mechanism), the equations for closing vectorial contours are written, and the kinematic conditions for determining velocities and accelerations and the associated linear systems are solved, which provides the field of speeds and accelerations. Graph Theory is applied at a kinematic level and not at a dynamic level, as in previous studies. A practical application for the kinematic analysis of the control mechanism of a light aircraft illustrates the proposed method.

RESEARCH CONCERNING THE STATIC BALANCING OF A MULTILOOP LINKAGE

In the paper a method for achieving the total static balancing of a linkage with two independent loops is presented. There are also analyzed two solutions for partial static balancing of the studied linkage. Finally, a series of results of the simulations performed in the studied balancing cases are given.

The Effect of the Optimization Selection of Position Analysis Route on the Forward Position Solutions of Parallel Mechanisms

The forward position solution (FPS) of any complex parallel mechanism (PM) can be solved through solving in sequence all of the independent loops contained in the PM. Therefore, when solving the positions of a PM, all independent loops, especially the first loop, must be correctly selected. The optimization selection criterion of the position analysis route (PAR) proposed for the FPS is presented in this paper, which can not only make kinematics modeling and solving efficient but also make it easy to get its symbolic position solutions. Two three-translation PMs are used as the examples to illustrate the optimization selection of their PARs and obtain their symbolic position solutions.

Type Synthesis of Variable Compression Ratio Engine Mechanisms

Type synthesis of two-degrees-of-freedom (DOF) planar mechanisms has been carried out using graph theory to determine the possible kinematic structures of variable compression ratio (VCR) engine mechanisms with two to three independent loops, and has resulted in the structures of 87 mechanisms satisfying search specification. By applying evaluation criteria to the enumerated mechanisms, the kinematic structures of three mechanisms are selected as suitable VCR engine mechanisms and verified by analysis results. In this research, VCR engine mechanisms with revolute joints and only one prismatic joint are enumerated, and the basic method to determine the VCR engine mechanisms with higher pairs is discussed. The procedure used in this research can be utilized to determine the kinematic structures of desired mechanisms and the results can be used as an atlas of two-DOF adjustable slider-crank 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.

STRUCTURAL SYNTHESIS OF ACTUATORS OF STIRRED TANKS WITH IRREGULAR MOTION OF IMPELLER

Предложено синтезировать зубчатые исполнительные механизмы перемешивающих устройств с неравномерным движением рабочего органа. В качестве метода синтеза применена структурная математическая модель в виде системы уравнений, описывающей взаимосвязи между количественным и качественным составом звеньев n и кинематических пар p будущего механизма, его подвижностью W, количеством замкнутых независимых контуров k, присоединений к стойке S и другими структурными параметрами. Начальные условия заданы с целью получения одноподвижных (W 1) плоских (П 3) механизмов с одним (k 1) и двумя (k 2) замкнутыми независимыми контурами. По результатам решения системы уравнений построены две схемы механизмов зубчатая передача (p1 2 p2 1 n2 2 S 2) и планетарный механизм с внешним зацеплением (p1 3 p2 2 n2 2 n3 1 S 3). Анализ синтезированных схем показал, что применение в их составе эллиптических зубчатых колес позволяет получить различные виды неравномерного движения выходного звена и, соответственно, закрепленного на нем рабочего органа. Преимущества предлагаемых перемешивающих устройств простота проектирования, надежность и компактность. It is proposed to synthesize gear actuators of stirred tanks with irregular motion of the impeller, since they allow providing higher intensity of mixing in the reactor. As a synthesis method, a structural mathematical model is used in a system of equations form that describes the relationship between the quantitative and qualitative composition of the links n and kinematic pairs p of the future mechanism, its mobility W, the number of closed independent loops k and connections to the rack S and other structural parameters. The initial conditions are specified with the aim of obtaining oneDOF (W 1) flat (P 3) mechanisms with one (k 1) and two (k 2) closed independent loops. Based on the results of solving the system of equations, two schemes of mechanisms were constructed: a gear (p1 2 p2 1 n2 2 S 2) and a planetary mechanism with external gearing (p1 3 p2 2 n2 2 n3 1 S 3). The analysis of the obtained schemes showed that the use of elliptical gears in their schemes allows to obtain various types of irregular motion of the output link and, accordingly, the impeller fixed on it. The advantages of the proposed stirred tank actuators are ease of design, reliability and compactness.

Enhanced Dynamic Set-point Weighting Design for Two-Input-Two-Output (TITO) Unstable Processes

Control of unstable systems with time delays usually result in overshoots in the closed loop responses. The intricacy involved in multivariable unstable processes further makes the problem more challenging. In industry, set-point weighting is one of the recommended methods to minimize the overshoot. However, design of the set-point weighting parameters determines the percentage of minimization of the overshoot. In this paper, a method is proposed to design the set-point weighting parameters for unstable multivariable processes which is relatively simple and also reduces the overshoot. Weighting is considered for both proportional (β) and derivative (γ) terms in the PID control law. In the closed loop relation for set-point tracking, the coefficients of ‘s’ and ‘s3’ both in the numerator and denominator are made equal in order to find dynamically β and γ. The obtained expressions for β and γ are simple and dynamically depends on the controller parameters and are applied to TITO systems in present work. Decouplers are used in TITO systems mainly to reduce the interaction between the loops so that they can be viewed as independent loops. Decoupler design suggested by (Hazarika and Chidambaram [1] has been used in this work and two TITO unstable processes with time delays are illustrated here. Comparison with the reported methods available in literature verifies that the proposed method gives improved closed loop performance.

Isomorphism Detection of Planar Kinematic Chains With Multiple Joints Using Information Theory

Isomorphism (structural similarity) of kinematic chains (KCs) of mechanisms is an important issue in the structural synthesis, which must be identified to avoid the duplicate structures. Duplication causes incorrect family size, i.e., distinct KCs with a given number of links (n) and degree of freedom (dof). Besides simple joints kinematic chains (SJKCs), multiple joints kinematic chains (MJKCs) are also widely used because of their compact size and the methods dealing with such KCs are few. The proposed method deals with two different structural invariants, i.e., primary structural invariants (provide only the necessary condition of isomorphism), such as link connectivity number (LCN) of all the links, link connectivity number of chain (CCN), joint connectivity number (JCN) of all the joints, and joint connectivity number of chain (JCNC), and secondary structural invariants (provide the sufficient condition of isomorphism), such as power transmission (P) and transmission efficiency (Te). Primary structural invariants are calculated using a new link–link connectivity matrix (LLCM), whereas secondary structural invariants are calculated using the concept of entropy of information theory. The method has been successfully tested for 10 and 11 links MJKCs (illustrative examples taken in the paper) and for the families of 18 MJKCs with 8 links, 2 MJs, 1-dof, and 3 independent loops; 22 MJKCs with 8 links, 1 MJ, 1-dof, and 3 independent loops; and 83 MJKCs with 9 links, 1 MJ, 2-dof, and 3 independent loops.