Seven-link Mechanism Research Articles

Gravity Balancing of a Two-Degree-of-Freedom Parallel Robotic Platform With Variable Payloads

Abstract This paper presents a gravity-balancing method for a two-degree-of-freedom (2-DoF) parallel robotic platform with variable payloads. The robotic platform is constructed with a parallelogram-based five-bar parallel mechanism, and it is gravity balanced by adopting a pair of gear-spring units (GSUs). Each GSU is formed by a geared seven-link mechanism with a tension spring. The parameters of the GSUs are realized from an analytical solution for approximate gravity balancing. The significance of the proposed method is that it can work with a range of payloads via energy-free adjustment and enables a choice in spring stiffness. In this paper, theoretical and practical models are provided to demonstrate the effectiveness of the proposed method. The simulation results showed that the actuator torque of a robotic platform with different payloads could be reduced by 98.2% with gravity balancing. Experimental tests with a prototype were conducted in which the measured driving force of the robotic platform along a trajectory showed a reduction of 87.1%.

On the Study of the Basic Design Parameters of a Seven-Link Spatial Mechanism of a Part Processing Machine

A design of a spatial seven-link mechanism with rotational kinematic pairs of a part processing machine without redundant constraints is presented. The principle of operation of the mechanism is described. The mechanism structure is studied using elements of kinematic analysis and SolidWorks CAD. Expressions for the determination of rational ratios of link lengths are derived that provide failure-free operation of the mechanism.

Kinematic and Static Analyses of the Pedaling by Means of New Slider-Crank Mechanism

A slider-crank mechanism whose coupler curve is the approximate ellipse is designed so that a man may perform the pedaling of the elliptical motion of the foot. Because the thigh, the shank and the foot constitute the three-link chain, the system of a man and the bicycle with the slider-crank pedal mechanism is the planar seven-link mechanism with two degree freedom. The system of a man and the ordinary bicycle is the planar five-link mechanism with two degree freedom. Kinematic characteristics of these systems are analyzed with the given pattern of the pedal angle curve during a crank rotation. Then, the crank moment and the pin joint forces of these systems are calculated for given patterns of the hip moment and the knee moment during a crank rotation and the average crank moment are estimated. It makes comparative study of calculated and experiment results of the pedal force, the crank moment and physiological results of oxygen uptake and carbon dioxide output in usual crank pedaling and in slider crank pedaling.

Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach

Combining planar and spherical 4R chains generates three kinds of new discontinuously movable (DM) seven-link mechanisms. The mobility analysis is based on algebraic concepts of set theory. These mechanisms are called hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6RIP DM mechanisms. Their discontinuous mobility is explained employing the Lie group algebraic properties of the displacement set. Moreover, the same given spatial arrangement of joints can be linked in two ways constituting two distinct chains, which have a quite different mobility. One chain has two global degrees of freedom (d.o.f.), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of mobility with one d.o.f. Then the set of relative motions between any two specific links is not manifold but consists of the union of displacement one-dimensional manifolds. In general, when two or more subgroups are involved in a closed-loop chain, the discontinuous mobility can happen by changing the order of the kinematic pair linking.

Synthesis of a planar seven-link mechanism with variable topology for motion between two dead-center positions

An analytical method of synthesis of a planar seven-link mechanism with variable topology for motion between two dead-center positions is suggested. The method is useful to reduce the solution space. The proposed method is non-iterative. A complex number, dyadic approach of synthesis of mechanism for motion, path (with prescribed timing) and function generation is considered. An alternative choice for Phase-II is also suggested.

Synthesis of Spatial Mechanism with Consideration of Degree of Freedom of Mechanism

In this paper, a systematic synthesis of the optimum arrangements of links and pairs in spatial mechanisms with multiple moving closed circuits is studied with consideration of the degrees of freedom of the mechanisms. Namely, the conditions required to construct the mechanisms with multiple moving closed circuits are formulated. Moreover, mechanisms with multiple moving closed circuits are constructed with some basic links and open chains, obtaining the optimum arrangement of links and pairs. Based on the above analytical results, a synthesis system is proposed which determines the optimum arrangements of links and pairs. Finally, the types of spatial seven-link mechanisms which satisfy requirements of the above-mentioned basic links and open chains are synthesized to illustrate the method.

A Type Synthesis of Spatial Mechanism with Consideration of Degrees of Freedom of Mechanism.

In this paper, a systematic synthesis of the optimum arrangements of links and pairs in spatial mechanisms with multiple moving closed circuits is studied with consideration of the degrees of freedom of the mechanisms. Namely, the conditions required to construct the mechanisms with multiple moving closed circuits are formulated. Moreover, mechanisms with multiple moving closed circuits are constructed with some basic links and open chains, obtaining the optimum arrangement of links and pairs. Based on the above analytical results, a type synthesis system is proposed which determines the optimum arrangements of links and pairs. Finally, the types of spatial seven-link mechanisms which satisfy requirements of the above-mentioned basic links and open chains are synthesized to illustrate the method.

Dynamic Analysis of Spatial Mechanisms Using Dual Successive Screw Method and D’Alembert’s Principle

The method based on the application of the successive dual screw displacements and d’Alembert’s principle, is developed to perform kinetostatic and dynamic analysis of space mechanisms with lower kinematic pairs. The method is applied to demonstrate its usefulness in performing kinetostatic and dynamic analysis of single-loop, four-link, five-link, six-link and seven-link mechanisms with lower kinematic pairs.

Nine-link plane mechanisms for two-variable function generation—I. Systematics

Nine-link plane mechanisms come in for consideration for two-variable function generation when a satisfactory design is not obtained using the seven-link mechanism. In this paper, all the possible nine-link mechanisms that can be used for function generation are listed. These are arrived at by a simple device from one-freedom eight-link mechanisms, a complete list of the latter being already available. There are 17 such nine-link mechanisms. Significant double-pivot mechanisms derived from the above are also listed.

A Simplified Approach to Two-Freedom Linkages

The use of what are known as identical swing positions (identische Schwingenlagen) is shown to simplify considerably the synthesis of the plane seven-link mechanism to generate functions of two variables. The mechanism with a fixed double joint, suitably achieved, has a four-link loop and can be easily synthesized for the largest number of precision points (11) by the foregoing method without any restriction in principle on the nature of the function to be generated. Application of the method to mechanisms without a four-link loop is possible under certain restrictions on the nature of the function.

Synthesis of Seven-Link Mechanisms

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.