Planar Six-bar Linkages Research Articles

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.

A 2 degrees of freedom united propulsive mechanism for amphibious function inspired by frog's hindlimb

Abstract. Amphibious species of frogs are notable candidates to mimic for amphibious robotic design, as their swimming and sprawling locomotion is generated by the united propulsive mechanisms in which the hindlimbs play the dominant role. Although the propulsive system of frogs is not as complex as other amphibians, it is still difficult to employ the propulsive mechanism in robotic design due to the numerous degrees of freedom (DoF). This paper proposes a novel united propulsive mechanism to acquire the amphibious function inspired by the frog's hindlimb. The mechanism is a hybrid design combining a planar six-bar linkage, which is designed based on homotopy continuation and a spatial four-bar linkage. The DoF of the hindlimb-like mechanism are dramatically decreased to 2, with 1 each in the two sub-chains. Forward analysis is conducted to find the pose of the foot when two actuations are input. The improved analysis based on the geometrical features overcomes the multiplicity from the numerical computation. The inverse kinematic analysis is conducted to find the rotation of the input with a given pose of the foot. The aquatic function of the united propulsive mechanism is demonstrated based on the blade element theory, where the rotational speed and the projected area of the foot are fully active. The terrestrial function of the propulsive mechanism is validated with a specific gait.

Nonlinear dynamic behavior analysis of multi-linkage mechanism with multiple lubrication clearances

Clearance exists in mechanical equipment, which aggravates the friction and wear in moving pairs and reduces the use accuracy of mechanism. So as to reduce the impact of clearance on industrial equipment, lubricating oil is usually added to the clearance of moving pair. The lubricating oil can effectively reduce the collision and vibration between components and reduce noise. Previous studies mainly concentrated on the research of dry clearance joints, but less on clearance lubrication. At the same time, there is little research on nonlinear characteristic of lubrication clearance. For the sake of studying the impact of lubrication clearance with multiple revolute joints on mechanical system, the dynamic response and nonlinear characteristic of planar six-bar linkage are analyzed. The movement model of lubrication clearance is developed, and lubrication force of lubrication clearance is modeled by modified Pinkus–Sternlicht model. Dynamical model of lubrication clearance of planar six-bar linkage is established by Lagrange multiplier method. The impacts of lubrication, viscosity coefficient, clearance value and driving speed on dynamic of mechanism with lubrication clearance are explored. By drawing bifurcation diagram, phase trajectory diagram and Poincare map, the nonlinear characteristic of mechanism with lubrication clearance is studied.

Study regarding the implementation of an Ackerman steering geometry in MATLAB

In dynamic vehicle behavior the steering system has an important role. The vehicle stability, maneuverability depends on steering system characteristics. Majority of passenger vehicles uses the rack pinion steering linkage system. In this article, a simplified planar six-bar linkage model of the rack pinion steering system is presented. Kinematic relations are used to determine every linkage position in every possible situation. This simplified system contains a rack, tie rods, steering arms, and wheels. The six-bar linkage model is introduced in MATLAB SIMULINK. In the function of the rack displacement, the wheel angels are determined. The dimensions of this planar model can be estimated due to the minimum error between the calculated wheel angels for the rack and pinion system and an Ackerman principle based system with similar dimensions. For optimizing a system and for verifying the method numerical calculation are used.

A method for branch identification of planar six-bar linkages with sliding pairs

A method for branch identification of planar six-bar linkages with sliding pairs

Chaos vibration of pinion and rack steering trapezoidal mechanism containing two clearances

The multi-clearances of breaking type steering trapezoidal mechanism joints influences vehicle steering stability. Hence, to ascertain the influence of clearance value on steering stability, this paper takes the steering mechanism of a certain vehicle type as a prototype that can be simplified into a planar six-bar linkage, then establishes the system dynamic differential equations after considering the two clearances of tie rods and the steering knuckle arms. The influence of the clearance parameters on the movement stability of the steering mechanism is studied using a numerical computation method. Results show that when the two clearances are equal, the planar movement of the tie rods changes from period-doubling to chaos as the clearances increase. When the two clearances are 0.25mm and 1.5mm respectively, the planar movements of the two side tie rods come into chaos, causing the steering stability to deteriorate. Moreover, with the increase of clearances, turning moment fluctuates more intensively and the peak value increases.

Function generation with two loop mechanisms using decomposition and correction method

Method of decomposition has been successfully applied to function generation with multi-loop mechanisms. For a two-loop mechanism, a function y = f(x) can be decomposed into two as w = g(x) and y = h(w) = h(g(x)) = f(x). This study makes use of the method of decomposition for two-loop mechanisms, where the errors from each loop are forced to match each other. In the first loop, which includes the input of the mechanism, the decomposed function (g) is generated and the resulting structural error is determined. Then, for the second loop, the desired output of the function (f) is considered as an input and the structural error of the decomposed function (g) is determined. By matching the obtained structural errors, the final error in the output of the mechanism is reduced. Three different correction methods are proposed. The first method has three precision points per loop, while the second method has four. In the third method, the extrema of the errors from both loops are matched. The methods are applied to a Watt II type planar six-bar linkage for demonstration. Several numerical examples are worked out and the results are compared with the results in the literature.

A large ring deployable mechanism for space satellite antenna

With the development of space technology, new demands for satellite communications services, space and earth observations drive the requirement for large aperture space antennas. In order to meet the missions, this paper presents a kind of novel single mobility deployable ring mechanism based on a set of planar six-bar linkages. The ring mechanism has very high deploy/fold ratio, which is suitable for building large scale satellite deployable antenna. The mobile assembly of the ring structure and synchronous movement compatibility conditions are investigated, then the synchronization movement of the six-bar linkage modules can be realized by using close-loop cable and dual slider-crank mechanisms, which ensure the single mobility of the whole ring mechanism. Two types of driving mode for the deployable ring mechanism including cable driven and torsion spring driven are studied, and the high rigidity driving joints are designed. Finally, a ground experimental prototype of a 3.9 meter in diameter is fabricated to show the feasibility of the proposed mechanism, the deployment accuracy are also tested and the results show the good repeatability for the ring deployable mechanism.

A Task-Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With R- and P-Joints for Five-Position Realization

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

A Design System for Six-Bar Linkages Integrated With a Solid Modeler

This paper presents a design system for planar and spherical six-bar linkages, which is integrated with a solid modeler. The user specifies a backbone 3R chain in five task configurations in the sketch mode of the solid modeler and executes the design system. Two RR constraints are computed, which constrain the 3R chain to a single degree-of-freedom six-bar linkage. There are six ways that these constraints can be added to the 3R serial chain to yield as many as 63 different linkages in case of planar six-bar linkages and 165 in case of spherical six-bar linkages. The performance of each candidate is analyzed, and those that meet the required task are presented to the designer for selection. The design algorithm is run iteratively with random variations applied to the task configurations within user-specified tolerance zones, to increase the number of candidate designs. The output is a solid model of the six-bar linkage. Examples are presented, which demonstrate the effectiveness of this strategy for both planar and spherical linkages.

Optimisation Design of Six-Bar Double Dwell Mechanisms: A New Approach

This paper introduces a new approach for me-chanical design of planar six-bar linkages with rotary joints which produce two dwells in each cycle of the input crank. The approach builds on the concept of function generation in a simple manner. The synthesis problem is posed as a single-objective constrained optimisation problem. A genetic algorithm-based optimisation scheme, namely the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) has been used for solving the optimisation problem. The proposed method has been illustrated by means of an example problem from a recent contribution to literature. It is seen that the results compare favourably with the existing work.

A study of the instantaneous centers of velocity for the 3-dof planar six-bar linkage

This paper is a detailed study of the instantaneous centers of velocity (henceforth referred to simply as instant centers) for the three-degree-of-freedom (henceforth abbreviated as 3-dof) planar six-bar linkage. The paper focuses on graphical techniques, which only require a knowledge of elementary and analytic geometry, to locate the unknown (or secondary) instant centers. In addition, analytical techniques are provided to interpret the graphical concepts and confirm the new results. Several important theorems are proposed which relate to special cases where the secondary instant centers are either single points or infinite lines. The paper investigates points and lines at infinity and presents theorems to explain how secondary instant centers relate to each other when one, or more, are at infinity. There is an in-depth discussion of double points and double lines, that is, points and lines that map onto themselves, and several lemmas and theorems show how to obtain the number of double points and double lines for the 3-dof six-bar linkage. The results presented in this paper will prove useful in the kinematic analysis and synthesis of multi-degree-of-freedom planar linkages.

Discriminant method for the mobility identification of single degree-of-freedom double-loop linkages

This paper presents the first successful attempt that extends the discriminant method to the mobility analysis of non-bimodal linkages. The singularity condition and the joint rotation space are expressed and identified by the discriminant functions. The method is algebraic and the discriminant function is derived based on the form of equations essential for the displacement analysis of the linkage. Therefore, its applicability is not restricted by the type of joints or the physical appearance of the linkage. It is applicable to any single degree-of-freedom planar and spherical double-loop linkages regardless the choice of the input, output, or fixed link. It is also applicable to spatial linkages with the similar displacement equation form. The method is ideal for automated mobility rectification and is demonstrated with single-DOF planar six-bar linkages.

2203 平面リンク機構を用いた装着型歩行補助装置の開発(健康・福祉機器の開発,一般講演)

The devices have been developed for elderly or rehabilitants to assist walk in a form of wearing type with electric devices. But these wearable walkers are expensive for users because this walker includes plural actuators and control computers. And more, there is a problem that the weight of the walker increases. Therefore, we suggest a walker which enables low cost and light weight. Concretely, we push forward development of the wearable walker which does not need electric devices and can be controlled by one input. In this paper, we suggest the walker which is designed planar six-bar linkage and prove utility of the walker.

Creative mechanism design for a prosthetic hand

In this paper, an auxiliary methodology called the creative mechanism design is introduced into the innovation of gripping devices for prosthetic hands. This methodology is a systematic approach based on modification of existing devices for the generation of all possible topological structures of mechanisms and mechanical devices. An existing gripping device (Teh Lin ATG-5F prosthetic hand) constructed by a planar six-bar linkage with one degree of freedom is dealt with by using this methodology. Through the processes of generalization, number synthesis, specialization and particularization for the existing design, five new mechanisms are created in this study to apply to anthropomorphic prosthetic hands. The results show that the methodology for creative mechanism design is a powerful tool for creating new categories of mechanisms to avoid existing designs that have patent protection and can help designers in the conceptual phase. Also, this methodology is validated as a useful way to improve prosthetic hands for amputees.

Compound strut and planar six-bar linkage suspension systems

This paper reviews the properties and possible advantages of compound strut and related six-bar linkage suspension systems.