Synthesis Of Mechanisms Research Articles

Substantiation of rational design parameters of a crusher with two movable jaws

Purpose. Design engineering of the mechanism of a two-jaw crusher with a compound motion of the jaws, which ensures a change in the angle of gripping of pieces of material within a very small range. Methodology. In the work, a theoretical study on the fourth-class lever mechanism, as the basis of a two-jaw crusher, was performed using the Mathcad 15 software. The study was performed on a vector representation of the links of the hinged mechanism. The development and analysis of constructive solutions were performed using the Autocad software product, which reduces the risk of errors and increases the quality of the design process. Findings. The paper theoretically determines the rational geometric parameters of the two-jaw crusher with the optimal value of the nip angle, whose crushing chamber is formed by the closed loop circuit of the flat fourth-class lever mechanism and proposes a new constructive solution of the mechanism for adjusting the crusher opening with two movable jaws and the bottom mounting of eccentric nodes. The developed device in the form of separate blocks is made with the possibility of their simple assembly and disassembly, which ensures the rate and quality of replacing lining plates or surfacing restoration of the worn working surface of the jaws. The relative movement of the jaws ensures the crushing of pieces of material with the required crushing coefficient. The geometric parameters were obtained by the method of kinematic synthesis. The geometric parameters of the crushing chamber of the two-jaw crusher were determined theoretically; the dependence was obtained of the change in the nip angle on the height of the movable jaw over a period of movement and the change in the compression stroke, which ensures the force interaction of the working surface of the jaws with the material. Originality. It is proved that the quadrilateral closed circuit of the fourth-class lever mechanism can be used as a crushing chamber of a two-jaw crusher. Two links of a closed circuit operate as jaws which break pieces of material. At the same time, the nip angle can vary within fairly narrow limits, ensuring the optimality of the crushing process. It was established that the considered option of the fourth-class six-link mechanism geometry has only two folds. An algorithm is presented for searching for assemblies with the purpose of identifying those that are closely adjacent. Practical value. The results of the conducted research provide the theoretical background and the algorithm for determining the optimal parameters of a two-jaw crusher which can be used at the stage of designing similar crushers. The developed design solution for adjusting the crusher opening expands the scope of application of double-jaw crushers. The obtained dependences of the change in the angle of inclination and the working surface of the jaw over a period make it possible to develop a rational mode of crushing the material

Task-driven geometric synthesis method of a bistable compliant mechanism for the rigid guidance problem

Abstract. Compliant bistable mechanisms are specialized mechanisms that have specific self-locking characteristics in two positions. They are widely used in aerospace, micro-electromechanical systems, and high-precision manufacturing. The coupling of kinematic with elastomechanical behaviors of compliant mechanisms, known as kinetostatics, increases the difficulty of synthesizing compliant mechanisms. Currently, most research relies on optimization approaches to find compliant mechanisms that meet motion requirements. To address this challenge, this paper proposes a geometric synthesis method for compliant bistable mechanisms to solve the rigid guidance problem. The pole similarity transformation characteristics of planar beams and the static equilibrium characteristic of bistable mechanisms at stable positions are utilized to decouple the kinematic synthesis and static analysis. The proposed method introduces a task-driven synthesis process, where the critical structural parameters in compliant mechanisms are determined based on the desired guidance positions of motion tasks. This approach eliminates the need for a tedious and time-consuming iterative optimization process. The resulting bistable mechanisms have two stable positions that correspond to the desired guidance positions of the motion task. To illustrate the effectiveness of the geometric synthesis method, a two-position problem of a compliant bistable mechanism is provided as an example.

Kinematic synthesis of the Gough-Stewart platform in ADAMS and MATLAB

Kinematic synthesis of the Gough-Stewart platform in ADAMS and MATLAB

Solving the QLY Least Squares Problem of Dual Quaternion Matrix Equation Based on STP of Dual Quaternion Matrices

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation AXB+CYD≈E, where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH-representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation AXB+CYD≈E. The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method.

Dynamic Analysis of Planar Mechanism in Numerical Methods

In kinematic synthesis and analysis of planar mechanisms the designer must define a geometry and set of motions for a design task. Then it is logical to determine the forces or torques in order to create such motion in the system, which means finding out a convenient approach to solving for the forces and torques that result from our kinematic system in such a way as to provide the designed accelerations. This task is called dynamic force analysis (or kinetic analysis). Many numerical methods to determine the position, velocity, and acceleration of a planar mechanism are introduced and applied successfully, for example, using the transformation matrix. To solve fully kinetic problems for a planar mechanism, it is necessary to establish a simple and easy procedure that determines the forces or torques maintaining the motion in the system with the help of a computer. This paper will focus on how to determine the forces or torques acting on the planar mechanism by numerical method when acceleration and dynamic properties of the linkage are known. Some of the chosen examples shown here aim to demonstrate in detail the numerical solution for dynamic force analysis. The paper’s purpose is not to demonstrate novelty, but to propose a new approach that can be applied to machinery design projects for students. University students can consult the content of this paper to carry out kinematic and kinetic analysis of planar mechanisms using this numerical method, as opposed to the traditional vector drawing method that is widely used.

Kinematic synthesis and mechanism design of a six-bar jumping leg for elastic energy storage and release based on dead points

Small jumping robots widely adopt complex catapult mechanisms. This paper presents a novel jumping strategy using dead point instead of traditional catapult mechanisms, achieving efficient energy storage and release without increasing mechanical complexity. Single degree-of-freedom (DOF) planar six-bar linkages are widely used in bionic mechanism design due to their simple control and strong design flexibility. However, their complex configuration and numerous parameters make it challenging to carry out multi-objective and multi-constraint designs. In this paper, a design method of single DOF six-bar linkages based on dead-point constraints is proposed to design a frog-inspired leg mechanism. By enumerating the basic configuration atlas and using a stepwise closed-loop method, initial value screening is completed to improve the efficiency of objective function optimization. The dead-point constraints are simplified with graphical geometric properties. The resulting mechanism satisfies multiple objectives and constraints, including shape, motion posture and trajectory, demonstrating the feasibility of the method. Simulations and experiments confirmed the excellent jumping performance of the 147.1-g prototype, with a jump height of 8.55 times leg length and an energy-storing capacity of 35.39 J/kg.

Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators

Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

A Kinematic Synthesis Methodology for P-Drivable Spatial Single Degree-of-Freedom Mechanisms to Avoid Singularities

Abstract For a single degree-of-freedom spatial mechanism, a reference frame attached to any of its links produces a continuous motion of this frame. Given the progression of this frame from the start through the end of the mechanism’s motion, this paper seeks to identify specific points relative to this moving reference frame. The points of interest are those that can be coupled with a second point determined in the fixed frame to act as the end joint locations for a spherical–prismatic–spherical (SPS) driving chain. If the selection of the point pair is made such that the change in distance between them as the mechanism moves is strictly monotonic, then the SPS chain they define is potentially capable of driving the mechanism over the desired range of motion. This motion is referred to as locally P-drivable because a global solution is not ensured by the process proposed herein. This synthesis process can avoid singularities encountered by actuating the mechanism at one of its original joints. The proposed approach enables the dimensional synthesis of a single degree-of-freedom mechanism to focus on creating circuit-defect-free solutions without concern for potential singular positions. The actuating chain can then be determined as a separate step in the synthesis process. This paper also considers motions that are not P-drivable and the specialization to planar systems with the synthesis of a P-drivable revolute–prismatic–revolute (RPR) chain.

Geared Linkage driven by Linear Actuator used for PV Platform Azimuth Orientation

. To gain more solar energy the photovoltaic converter must be tracked relatively to the sun movement. The majority of the tracking systems use complicated and costly rotating mechanisms to build large angular strokes. This paper presents a new type of geared linkage composed of a triangular linkage fitted with a planetary gear pair able to reach high angular strokes. This linkage is used as basic mechanism for the azimuth tracking of a photovoltaic platform. The kinematic synthesis of the linkage shows that the azimuth angular stroke increases with the planetary gear internal ratio |i0|. The linkage is further implemented for an azimuth mono-axial tracked PV module located in a mountain location (case study - Brasov, Romania). Through numerical simulations, the amount of direct solar radiation on the PV module and the tracking efficiency are evaluated.

An Integrated Kinematic Mapping and Fourier Method to Design Spherical Coupled Serial Chain Mechanisms for Single-Joint Rehabilitation

Abstract Robotic devices are capable of reducing the physical burden on rehabilitation therapists and providing training programs of good repeatability, high efficiency, and high precision. When designing the kinematic structure for rehabilitation robots, there has been a growing interest toward one-degree-of-freedom (DOF) end-effector mechanisms due to their simpler structure and less complicated control algorithms. Compared with current one-DOF mechanism designs that are mainly customized for multi-joint robotic training, spherical coupled serial chain (SCSC) mechanisms are proposed in this paper to specifically deliver the single-joint robotic training, which is of equal importance to the effective physical recovery. Using kinematic mapping theory, the end-effector motion of SCSC mechanisms can be naturally transformed to two trigonometric curves composed of finite Fourier series in two separate planes of the image space. This novel formulation helps to establish an analytical and direct relationship between the design parameters of the SCSC mechanism and the harmonic parameters of the image-space representation of the task rehabilitation motion. The result is a simple and effective method for kinematic synthesis of SCSC mechanisms for generation of single-joint motion with an arbitrary number of spherical poses. An example of designing SCSC mechanisms for shoulder-joint rehabilitation is presented at the end of this paper to illustrate the feasibility of the proposed method.

A New Kinematic Synthesis Model of Spatial Linkages for Designing Motion and Identifying the Actual Dimensions of a Double Ball Bar Test Based on the Data Measured

This paper presents the new synthesis models of spatial linkages for designing measurement motion functions and ranges and identifying the actual dimension parameters. The spatial five-bar linkage is first introduced for the kinematic model of a double ball bar test of a two-axis rotary table. To design the ideal measurement motion and motion range of the double ball bar test, a novel saddle synthesis model of a spatial four-bar linkage RRSS is readily presented. Based on the output data measured from the double ball bar test, a new saddle synthesis model of a spatial five-bar linkage RRSPS is logically proposed for identifying their actual dimensions. Finally, three test cases and their results indicate that the new synthesis models presented in the paper can conveniently and efficiently calculate the measurement motion function and range and accurately identify the actual dimensions of the double ball bar test, which provides a suitable mathematical model for improving the accuracy of the double ball bar tests of a two-axis rotary table of machine tools.

Expansion of MK Circle Theory for Dyads and Triads

The MK circles represent a kinematic synthesis tool for the dimensional synthesis of planar dyads. The tool is uniquely useful in its ability to both find specific dyad solutions and help the designer visualize numerous potential dyad pivot locations in the solution space. Here, the existing understanding of MK circles is summarized for three and four specified motion positions and extended for additional positions. Then the technique is expanded to show its application to MKT circles for triad synthesis, including solution space visualization, ground pivot specification, and multi-loop synthesis of complex mechanisms. These methods are illustrated by a unifying example that provides a sample procedure for applying the MK/MKT circles, and implements each of the aforementioned techniques. The interchangeability of loop-based synthesis approaches is demonstrated by comparing the new methodology to the compatibility linkages technique.

OPTIMIZATION METHODS IN CALCULATIONS OF MECHANISMS OF VEHICLES OF TRANSPORT

Purpose. The optimal design of vehicle mechanisms is a detailed review and evaluation of the scientific and technical literature and individual publications on the methodology for optimizing the inherent calculations of these types of mechanical structures. The main purpose of this review material is to consider a number of directions for designing mechanisms of means of transport, especially highlighting the use of optimization methods. Research in the field of designing mechanisms is carried out in two directions: by the synthesis method according to given provisions and by the method of mathematical programming. Methods. Methods for the synthesis of hinged-lever mechanisms can be divided into two groups. In the first one, methods of approximation of functions are used, in the second one, optimization methods. The search for the optimal solution in the second group means the simultaneous search for the correct formulation of the problem, in which the parameters of the mechanisms should be sought under conditions of the best satisfaction of the requirements of the technological process. The problems of optimal design of mechanisms most often continue to be formulated as problems of the best approximation of functions. Optimization synthesis is a relatively new direction in the synthesis of lever mechanisms. Optimization synthesis is carried out on the basis of nonlinear optimization methods. At present, the complexity and complexity of the problems that arise and require solution in the process of designing mechanisms have significantly increased. A certain amount of research has been carried out within the framework of the classical theory of finite and infinitely small plane displacements. In these works, the theory of spatial motion of a general form is developed in detail and applied to the problems of kinematic synthesis. Results. Since the simplex method is quite effective in solving problems of linear programming, it became the founder of a number of methods of sequential linearization or methods of secant planes for solving nonlinear programming. Practical significance. With an extensive list of modern literature and scientific publications on the synthesis of mechanisms and mathematical programming, a complete chronological review of the achievements of the last decade would be quite loud. Therefore, individual trends in the synthesis of mechanisms were only noted, focusing on the desire to obtain a “better” design, taking into account practical requirements. The synthesis of mechanisms is an area in which the application of mathematical programming methods is quite promising due to their free formulation. The constraints and requirements of engineering practical problems can often be taken into account in forms consistent with the data of modern methods. The main purpose of this study is to make widely known the achievements in the two fields with the hope that currently existing optimization tools will be applied to these synthesis problems and that, conversely, the optimization tools will be further improved as a result of research on the design of vehicle mechanisms. This will contribute to a better understanding and accelerated development of both mechanisms calculation methods and optimization methodology.

Kinematic Design of Adaptive Control Adjustable Stroke Piston Pump for Automated Lubrication System

Lubrication is done either manually or using automatic systems, the purpose of the automatic lubrication system is to provide certain amount of lubricant at given time to the machines the proposed work is based on auto control variable displacement pump and referencing to literature survey it is a novel work involves, an innovative kinematic link base stroke changing mechanism. The stoke variation mechanism serves to alter the stroke of the piston pump in a controlled manner to control the flow rate of the pump precisely. The present work pertains to the design theoretically and kinematic synthesis of the components of the kinematic linkage. The theoretical design of the kinematic linkage is done using graphical method by overlay method, and the analysis of the kinematic linkage is done using adam’s software. The linkage motion for various angle of crank and corresponding output link are derived from this kinematic synthesis. The kinematic analysis of the linkage is done in using adam’s software and the motion study of the link is done to determine the parameters velocity of link and acceleration of link used in the mechanism.

Two-Position Synthesis of the Four-Bar Planar Linkage Mechanisms Using Artificial Neural Networks

The four-bar linkage mechanism is a fundamental and widely recognized mechanism with diverse applications, including various vehicle components, rehabilitation robotics, and rotary and reciprocating engines. Traditional textbooks introduce graphical and analytical solutions for the kinematic synthesis problem of the four-bar mechanism in different positions, while research articles explore its applications in various fields. Recently, artificial neural network (ANN) methods have gained popularity across different research domains. Researchers have proposed different solution approaches using ANN algorithms for the inverse and forward kinematic analysis problems of these mechanisms. However, the specific use of ANN algorithms for solving the two-position kinematic synthesis problem of the four-bar planar linkage mechanism has not been explored yet. This study aims to address this gap by introducing a solution for the two-position kinematic synthesis problem of the four-bar planar linkage mechanism using an artificial neural network algorithm. The Levenberg-Marquardt backpropagation neural network algorithm is chosen due to its speed, combination of Gauss-Newton training algorithm and steepest descend method, and ability to provide stable convergence of the training error. The neural network algorithm is trained, validated, and tested using a total of 50 randomly split data sets. Additionally, an additional test is conducted using all 50 data sets to evaluate the performance of the trained neural network algorithm. The study presents and discusses the results of the artificial neural network algorithm solution.

Kinematic synthesis and optimization design of a rice pot seedling transplanting mechanism

To achieve the precise operation trajectory and posture required for pot seedling transplanting and solve the problem that the partial reversal of the transplanting arm’s output in the double planet carrier transplanting mechanism, which is unconducive to the realization of the seedling pushing action, a motion synthesis method for a double planet carrier gear train mechanism with attitude constraints based on the output angle and four exact task poses is proposed. First, the ideal transplanting trajectory is planned according to the transplanting agronomic requirements, and the position and attitude information of the four key points on the ideal trajectory are extracted as the constraints of the mechanism design. Then, based on the relative displacement equation, a comprehensive design equation of the motion of the plane 3R mechanism (simplified model of the transplanting mechanism) about the output rotation angle and the precise four pose constraints is established, and the mechanism parameters that meet the constraint requirements are obtained by solving the multicellular homotopy method. A mathematical model of the roundness of the non-circular gear was also established, and the roundness of the transmission non-circular gears in the gear-train transplanting mechanism was optimized by using the genetic algorithm. Finally, the structural design, virtual simulation, and experimental analysis of the double-planet carrier gear train transplanting mechanism were completed. The results show that the actual trajectory and attitude are consistent with the theoretical design, and when then the mechanism was under the transplanting efficiency of 120 and 180 plants/min, the success rates of picking seedlings were 91.53% and 87.46%, respectively, meeting the design requirements.

Robust Multilegged Walking Robots for Interactions With Different Terrains

Abstract This paper explores the kinematic synthesis, design, and pilot experimental testing of a six-legged walking robotic platform able to traverse through different terrains. We aim to develop a structured approach to designing the limb morphology using a relaxed kinematic task with incorporated conditions on foot-environments interaction, specifically contact force direction and curvature constraints, related to maintaining contact. The design approach builds up incrementally starting with studying the basic human leg walking trajectory and then defining a “relaxed” kinematic task. The “relaxed” kinematic task consists only of two contact locations (toe-off and heel-strike) with higher-order motion task specifications compatible with foot-terrain(s) contact and curvature constraints in the vicinity of the two contacts. As the next step, an eight-bar leg image is created based on the “relaxed” kinematic task and incorporated within a six-legged walking robot. Pilot experimental tests explore if the proposed approach results in an adaptable behavior which allows the platform to incorporate different walking foot trajectories and gait styles coupled to each environment. The results suggest that the proposed “relaxed” higher-order motion task combined with the leg morphological properties and feet material allowed the platform to walk stably on the different terrains. Here we would like to note that one of the main advantages of the proposed method in comparison with other existing walking platforms is that the proposed robotic platform has carefully designed limb morphology with incorporated conditions on foot-environment interaction. Additionally, while most of the existing multilegged platforms incorporate one actuator per leg, or per joint, our goal is to explore the possibility of using a single actuator to drive all six legs of the platform. This is a critical step which opens the door for the development of future transformative technology that is largely independent of human control and able to learn about the environment through their own sensory systems.

Development of an optimally designed real-time automatic citrus fruit grading–sorting​ machine leveraging computer vision-based adaptive deep learning model

Conventional automation approaches for postharvest operations are plagued by time and data inefficiency seldom leading to suboptimal solutions. Automatic machines often require highly skilled software professionals for calibration and reconfiguration thus making the technology prone to high costs. Contemporary sensors and smart devices capable of handling deep learning image analytics have been employed in the present study for the development of an automatic machine that performs postharvest operations, like—washing, vision-based sorting and weight-based grading of citrus fruits with much reduced human effort while achieving excellent performance for the designated tasks. Accuracy of performance was ensured by the optimal design of mechanical components carried out by kinematic synthesis and dimensional analysis. The machine was equipped with an effective custom lightweight CNN model “SortNet” that was designed and tuned to carry out vision-based classification of citrus fruits into “accept” and “reject” based on surface characteristics. SortNet was less complex and took less computational time while exhibiting comparable accuracy with respect to existing state-of-the-art pre-trained deep learning models. An embedded system operated by a single-board computer was used in the weight grading section for segregating fruits based on three weight categories. Evaluation, realization and transferability of the above said strategy was demonstrated by the real hardware with physical actuators working in real-time to serve as proof-of-concept for a sustainable solution to postharvest automation of citrus fruits.

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories.

Reformulation of Theories of Kinematic Synthesis for Planar Dyads and Triads

Methods for solving planar dyads and triads in kinematic synthesis are scattered throughout the literature. A review of and a new compilation of the complex number synthesis method for planar dyads and triads is presented. The motivation of this paper is to formulate uniform solution procedures, pointing out the commonalities of various approaches and emphasizing a consistent method for synthesizing mechanisms defined by specified precision positions. Particular emphasis is given to the solution method using compatibility linkages. The textbook Advanced Mechanism Design Vol II by Erdman and Sandor (1984) only includes a small portion of the available information on this method, and several researchers have added to the basic knowledge in the years since. In some cases, the approach and nomenclature were not consistent, yielding a need to describe and chart a generic formulation and solution procedure for dyads/triads using compatibility linkages and solution structures. The present method offers benefits for solving for exact dyad/triad solutions for complex multiloop mechanisms and could be a promising tool for reducing the computational load of finding complex mechanisms, and for visualizing properties of the solution space.