Eight-bar Linkage Research Articles

A Dataset of 3M Single-DOF Planar 4-, 6-, and 8-bar Linkage Mechanisms with Open and Closed Coupler Curves for Machine Learning-Driven Path Synthesis

Abstract In recent years, there has been a strong interest in applying machine learning techniques to path synthesis of linkage mechanisms. However, progress has been stymied due to a scarcity of high-quality datasets. In this paper, we present a comprehensive dataset comprising nearly three million samples of four-, six-, and eight-bar linkage mechanisms with open and closed coupler curves. Current machine learning approaches to path synthesis also lack standardized metrics for evaluating outcomes. To address this gap, we propose six key metrics to quantify results, providing a foundational framework for researchers to compare new models with existing ones. We also present a Variational AutoEncoder based model in conjunction with a k-nearest neighbor search approach to demonstrate the utility of our dataset. In the end, we provide example mechanisms that generate various curves along with numerical evaluation of the proposed metrics.

Synthesis and Analysis of Plane–Space Switching Mechanisms Based on a Plane-Symmetric Eight-Bar Linkage

Abstract This paper proposes a novel synthesis method for constructing plane–space switching mechanisms based on the symmetric plane of the regular prism. First, the structure equation and motion characteristic of plane-symmetric eight-bar linkage are presented. Then, the plane-symmetric seven-bar linkage and rhombic Bricard linkage are obtained by locking the joint of the eight-bar linkage. Four types of plane–space switching mechanisms are constructed based on the synthesis method and switching linkage units. These switching mechanisms can expand completely into planar configurations and fold completely into spatial configurations. Subsequently, the kinematics of the coupled branch chain is analyzed, through which the folded and contractive characteristics of the mechanism are revealed. Then, the concept of the distributed circle of joints is proposed, and the enveloping performance of the mechanism is approximately analyzed. This paper provides a new idea and synthesis method for designing new deployable mechanisms.

Synthesis and optimization of an eight-bar linkage mechanism for seat suspensions

The work presents the analysis and synthesis of an eight-link mechanism for industrial seat suspension, followed by a numerical optimization of the design under specific technical requirements. Even though the eight-bar linkage mechanism is a well-known architecture, it has few applications in seat suspensions, and it shows interesting features compared with more traditional scissor systems. It is possible to exploit this mechanism, provided that is correctly designed, to achieve a seat suspension system, which grants a large quasi-perfect vertical motion, without the need of prismatic couplers, which are often a weak point in off-highway application due to their maintenance issues and cost. Firstly, the problem was tackled analytically in order to obtain the general set of equations and verified numerically with a multibody solver. Secondly, to choose the best solution for the application, we carried out an optimization of the system, aimed at minimizing the horizontal displacement of the seat along with granting the desired vertical travel needed. The results are both a general design procedure to optimize under specific constraints the eight-bar linkage for seat suspensions problems and a detailed design and possible embodiment of a seat suspension systems with application in the agricultural field.

The hybrid synthesis of a multi-functional eight-bar linkage with a translational actuator

Linkage synthesis includes three types of task specifications, which are motion generation, function generation and path generation. Generally, the three syntheses are treated separately. However, in some situations, linkage needs to complete two types of tasks, called hybrid tasks, simultaneously. In this paper, we present an analytical method to synthesize a multi-functional eight-bar linkage with a translational actuator to complete a hybrid task. The linkage can pass through 5 task positions for function generation and 5 task positions for motion generation simultaneously. To avoid highly nonlinear polynomial design equations, the linkage is separated into three loops to synthesize. The strategy of kinematic performance verification is proposed to obtain a non-defect linkage. Finally, a novel variable wing sweep mechanism for unmanned air vehicle is designed by using the multi-functional eight-bar linkage, which also validates the hybrid synthesis method. The result of this study provides a new design idea for linkage design.

An Automatic Generation Method for Determining the Crank Existence Region of an Eight-Bar Linkage with a Six-Bar Group

An Automatic Generation Method for Determining the Crank Existence Region of an Eight-Bar Linkage with a Six-Bar Group

Optimum design and analysis of a novel planar eight-bar linkage mechanism

Planar mechanisms are essential for many applications. The metal forming process is a vital application for industrial sectors such as automotive and space. Manufacturing precision and generating dwell motion are also important issues. These properties cannot be realized on conventional mechanical presses. Therefore, a novel single degree of freedom (1DOF) eight-bar planar mechanism was developed in this study. The main advantages of the new mechanism are slider balance and dwell motion without a servo motor. Thanks to these advantages, manufacturing difficulty and cost can be reduced. In this study, the new mechanism was modeled kinematically and verified. An optimization methodology was also presented for determining the mechanism dimensions. In order to achieve the desired dwell motion, dimensions of the mechanism for three cases (stroke capacities with 60 mm, 600 mm (crank length ≤ 300 mm), and 600 mm (crank length ≤ 250 mm)) were optimized by using the Genetic Algorithm (GA). The optimized dimensions were also compared kinematically, and the comparison results were shown. The best-optimized dimensions were determined based on the position, velocity, and acceleration simulations of the new mechanism.

Empirical Study of Constraint-Handling Techniques in the Optimal Synthesis of Mechanisms for Rehabilitation

Currently, rehabilitation systems with closed kinematic chain mechanisms are low-cost alternatives for treatment and health care. In designing these systems, the dimensional synthesis is commonly stated as a constrained optimization problem to achieve repetitive rehabilitation movements, and metaheuristic algorithms for constrained problems are promising methods for searching solutions in the complex search space. The Constraint Handling Techniques (CHTs) in metaheuristic algorithms have different capacities to explore and exploit the search space. However, the study of the relationship in the CHT performance of the mechanism dimensional synthesis for rehabilitation systems has not been addressed, resulting in an important gap in the literature of such problems. In this paper, we present a comparative empirical study to investigate the influence of four CHTs (penalty function, feasibility rules, stochastic-ranking, and ϵ-constraint) on the performance of ten representative algorithms that have been reported in the literature for solving mechanism synthesis for rehabilitation (four-bar linkage, eight-bar linkage, and cam-linkage mechanisms). The study involves analysis of the overall performance, six performance metrics, and evaluation of the obtained mechanism. This identified that feasibility rules usually led to efficient optimization for most analyzed algorithms and presented more consistency of the obtained results in these kinds of problems.

Innovative design of eight-bar linkage motorcycle suspension based on mechanism regeneration method

Motorcycles have high requirements on operation agility, steering accuracy and braking stability when running at high speed, and the core structure that determines the above performance lies in the suspension system. Therefore, this study uses the mechanism regeneration method to analyze the Duolever multi-bar linkage scissor front suspension of BMW and the eight-bar linkage rear suspension of Honda, and the topology matrix and generalized kinematic chain of the mechanism are obtained. Under the condition of meeting the design constraints, 12 kinds of eight-bar ten-pair combined kinematic chains can be gotten. After specifying the link types in turn, 17 feasible new eight-bar linkage motorcycle suspensions are finally realized. This study provides an efficient method for the independently design of the motorcycle suspension topology.

Design of a Continuum Mechanism That Matches the Movement of an Eight-Bar Linkage

Abstract This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force-deflection task for a compliant mechanism, our approach shapes the initial structure based on the kinematic synthesis of a rigid-body mechanism for the required movement, then the structure is shaped using finite element analysis to achieve the required force-deflection relationship. The result of this approach is a continuum mechanism with the same workpiece movement as the rigid link mechanism when actuated. An example illustrates the design process to obtain an eight-bar linkage that guides its workpiece in straight-line rectilinear movement. We show that the resulting continuum mechanism provides the desired rectilinear movement. A 210 mm physical model machined from Nylon-6 is shown to achieve 21.5 mm rectilinear movement with no perceived deviation from a straight-line.

Solution region synthesis methodology of planar eight-bar linkage for four specified positions of a 4R chain

The solution region methodology for solving the problem of four-bar linkage synthesis with four specified positions was extended to solve the problem of eight-bar linkage synthesis. The processes to build solution regions for synthesizing different types of eight-bar linkages are described, and the methods of building solution regions are divided into five types. First, the synthesis equation is derived, and the curve expressed by the synthesis equation is called the solution curve. Second, the process to build the spatial solution regions from the solution curves is detailed, and a new defect identification method is developed for building the spatial feasible solution region, which is a set of linkage solutions meeting four positions and excluding defects. Finally, linkage solutions that do not meet practical engineering requirements are eliminated from the spatial feasible solution region to obtain the useful spatial solution region. The examples demonstrate the feasibility of the proposed method. The proposed synthesis methodology is simple and easy to program, and provides reference for four specified position synthesis of other multi-bar linkages.

A class of N-sided antiprism deployable polyhedral mechanisms based on an asymmetric eight-bar linkage

An asymmetric eight-bar linkage is used as the basic unit to develop a group of N-sided antiprism (N⩾3) mechanisms. First, the geometric properties and kinematics equations of the asymmetric eight-bar linkage are investigated. When the kinematic conditions hold, an asymmetric eight-bar linkage and a single-plane or double-plane symmetric eight-bar linkage can be coupled. Second, the concept of axis groups is proposed, and virtual-center-based method is applied to construct a class of deployable polyhedral mechanisms based on N-sided antiprism polyhedrons; the motion bifurcation characteristics of the mechanisms are revealed by analyzing the singularity of the eight-bar linkages. These mechanisms may perform motion bifurcation in multiple different positions; therefore, these mechanisms are capable of having many different configurations that can increase their application potential for adapting to different tasks and working environments. Finally, the motion unit H is constructed based on the axis group and used as the deployable unit to synthesize a deployable mechanism with 120 loops based on a rhombic triacontahedron. Moreover, H can replace the double-plane symmetrical eight-bar linkage in other deployable polyhedral mechanisms to construct mechanisms with larger work space.

A novel methodology for determining the singularities of planar linkages based on Assur groups

In this paper, a simple and effective methodology for judging the singularities of planar linkages is presented, which is based on Assur groups. The methodology determines the geometrical configurations of the Assur groups in singularities. Based on the singularities of a simple two-bar group, the possible singularities of all Assur four-bar and six-bar groups are given by the concept of instant centers. Then the general process and rules of determining singularities are obtained and shown through several examples of the 1-DOF planar linkages. These linkages include the two six-bar linkages and the several eight-bar linkages composed of Assur six-bar groups. The singularities of them verify the proposed methodology, which reveals that the singularities of a linkage only depend on the Assur groups. Therefore, as long as the singularities of Assur groups are determined, all the possible singularities of the linkage composed of these groups can be determined. This methodology is independent of linkages, so it is universal for all planar multi-bar linkages which can be divided into these Assur groups.

Kinematic Synthesis and Design of the Robust Closed Loop Articulated Minimally actuated (CLAM) Hand

SUMMARYThe paper presents a comprehensive design process for the development of the minimally actuated Closed Loop Articulated Mechanical (CLAM) hand. Each of the fingers is designed as a planar one degree of freedom eight-bar linkage with an anthropomorphic backbone chain. The fingers movement is based on experimentally obtained physiological precision grasping task, with incorporated second-order task specifications, related to maintaining fingertip–body contact with a minimum number of fingers. Instead of actuating individual joints in each finger, the mechanism generates the desired anthropomorphic grasping trajectory using a single actuator in each finger. The paper offers not only details on multi-loop articulated hands design based on anthropometric data and physiological task with second-order effects for maintaining the object–fingertip contact, but also shows how this class of hands that have been considered mostly for adaptive grasping can be successfully utilized for precision grasping. The minimal number of fingers and actuators can simplify the control, resulting in a robust, lightweight, and cost-effective solution for the precision grasping of a variety of objects with different shapes and geometries.

Synthesis and analysis of Fulleroid-like deployable Archimedean mechanisms based on an overconstrained eight-bar linkage

This paper presents a novel intuitive synthesis approach for constructing Fulleroid-like Archimedean DPMs based on a Sarrus-like overconstrained spatial eight-bar linkage. Firstly, structure and the associated foundations of the eight-bar linkage are presented and characterized. Then, by integrating the eight-bar linkage into the Archimedean polyhedron bases, synthesis of a group of Fulleroid-like Archimedean DPMs is implemented; demonstrated by the design and construction of a Fulleroid-like deployable cuboctahedral mechanism and a Fulleroid-like deployable truncated tetrahedral mechanism. Subsequently, the mobility of these Fulleroid-like DPMs is verified through formulating the constraint matrices with Kirchhoff’s circulation law and the associated constraint graphs. Further, kinematics of proposed polyhedral mechanisms is derived with numerical simulations, leading to the motion characterization of the eight-bar linkage and the group of Fulleroid-like deployable Archimedean mechanisms.

A Sarrus-like overconstrained eight-bar linkage and its associated Fulleroid-like platonic deployable mechanisms

This paper, for the first time, presents an overconstrained spatial eight-bar linkage and its application to the synthesis of a group of Fulleroid-like deployable platonic mechanisms. Structure of the proposed eight-bar linkage is introduced, and constrain and mobility of the linkage are revealed based on screw theory. Then by integrating the proposed eight-bar linkage into platonic polyhedron bases, synthesis of a group of Fulleroid-like deployable platonic mechanism is carried out; which is demonstrated by the synthesis and construction of a Fulleroid-like deployable tetrahedral mechanism. Further, mobility of the Fulleroid-like deployable platonic mechanisms is formulated via constraint matrices by following Kirchhoff’s circulation law for mechanical networks, and kinematics of the mechanisms is presented with numerical simulations illustrating the intrinsic kinematic properties of the group of Fulleroid-like deployable platonic mechanisms. In addition, a prototype of the Fulleroid-like deployable spherical-shape hexahedral mechanism is fabricated and tested; verifying the mobility and kinematic characteristics of the proposed deployable polyhedral mechanisms. Finally, application of the proposed deployable platonic mechanisms is demonstrated in the development of a transformable quadrotor. This paper hence presents a novel overconstrained spatial eight-bar linkage and a new geometrically intuitive method for synthesising Fulleroid-like regular deployable polyhedral mechanisms that have great potential applications in deployable, reconfigurable and multifunctional robots.

Nonanthropomorphic exoskeleton with legs based on eight-bar linkages

This article presents the principles upon which a new nonanthropomorphic biped exoskeleton was designed, whose legs are based on an eight-bar mechanism. The main function of the exoskeleton is to assist people who have difficulty walking. Every leg is based on the planar Peaucellier–Lipkin mechanism, which is a one degree of freedom linkage. To be used as a robotic leg, the Peaucellier–Lipkin mechanism was modified by including two more degrees of freedom, as well as by the addition of a mechanical system based on toothed pulleys and timing belts that provides balance and stability to the user. The use of the Peaucellier–Lipkin mechanism, its transformation from one to three degrees of freedom, and the incorporation of the stability system are the main innovations and contributions of this novel nonanthropomorphic exoskeleton. Its mobility and performance are also presented herein, through forward and inverse kinematics, together with its application in carrying out the translation movement of the robotic foot along paths with the imposition of motion laws based on polynomial functions of time.

Bioinspired sprawling robotic leg and a path-planning procedure

This article shows the characteristics of a sprawling robotic leg inspired by the limb postures of certain reptilian animals known as sprawling-legged creatures. The main part of the robotic limb is based on the eight-bar Peaucellier–Lipkin linkage, and its main attribute is the ability to trace a true straight line, due to the rotational motion of the input link. However, when the eight-bar linkage is modified, it is capable of tracing true circular concave or convex arcs, when two of its constitutive links have distinct and precise lengths. This gives rise to the concepts of concavity and convexity, related to a robotic leg based on the Peaucellier–Lipkin mechanism, such as the one described herein. Our bioinspired robotic leg can trace concave or convex curves, as well as straight lines, making it a reptile-like robotic limb that is very similar to the natural one. We also introduce the concept of rotation center tuning, which refers to the ability of the leg to adapt its posture to the center of rotation of the entire walking machine, resulting in an easy and suitable gait process. The theoretical information is illustrated through the simulation of an example that provides a path-planning procedure, focusing on the rotation center tuning process and a walking gait. The example also includes the design of an elliptical path projected onto the cylindrical workspace and followed by the reptilian foot.

Bifurcated configurations and their variations of an 8-bar linkage derived from an 8-kaleidocycle

The paper presents an eight-bar linkage derived from a rotatable kaleidocycle, a hinged ring of eight regular tetrahedra with revolute joint axes along common edges. A thorough kinematics study of this eight-bar linkage is conducted with screw system approach and the kinematics closure equation is derived in a simplified way. The bifurcated motion of this two-degree-of-freedom linkage is explored in the joint space for the first time. Based on the sagittal planes of the joint space, the bifurcated sub-motions of a special line and plane symmetric Bricard linkage are analyzed.

An Algebraic Formulation for the Configuration Transformation of a Class of Reconfigurable Cube Mechanisms

Abstract. This paper presents an algebraic strategy for formulating the configuration transformation of a special class of reconfigurable cube mechanism (RCM) made by 23 cyclically connected sub-cubes. The RCM studied here is kinematically equivalent to a spatial eight-bar linkage having eight transformable configurations. In this paper, the reconfiguration characteristics of the RCM are figured out first. Then, the initial configuration of the RCM is described by a joint-screw matrix, from which all the consecutive joint-screw matrices that represent the configuration transformation of the RCM can be derived. An illustrative example is provided to determine the eight joint-screw matrices of an RCM at an initial configuration. This reconfiguration formulation is further applied to enumerate all feasible topological configurations of such a special reconfigurable mechanism. The results show that, for such a special kind of reconfigurable cube mechanisms, there is only one feasible initial topological configuration for the RCM to perform a complete cycle of reconfiguration.

Design Exploration and Kinematic Tuning of a Power Modulating Jumping Monopod

The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27 m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.