Optimization of Spherical Joint Attachment in Spatial Linkages

1988 ◽  
Vol 110 (4) ◽  
pp. 440-445 ◽  
Author(s):  
M. M. Stanisˇic´ ◽  
W. F. Mirusky
Keyword(s):  
Kinematic Analysis ◽  
Optimization Technique ◽  
Spherical Joint ◽  
Spatial Linkages ◽  
Four Bar Linkage

This paper presents the kinematic analysis and optimization technique required for the optimal attachment of a spherical joint (i.e., a ball in a socket) to the ground pivoted link of an RSSR spatial four-bar linkage. The optimization technique is a searching algorithm, which can be applied to the problem of optimal spherical joint attachment in other types of spatial linkages as well. This attachment optimization is necessary if the socket of the joint is to have its maximum ball retention capability. The optimization technique is illustrated by an example.

Kinematic Analysis of Spherical Four-Bar Linkages via the Inflection Cubic and Thales Ellipse

2015 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Special Interest ◽  
Kinematic Analysis ◽  
Vector Fields ◽  
Three Dimensions ◽  
Unique Point ◽  
Planar Case ◽  
Acceleration Vector ◽  
The Subject ◽  
Four Bar Linkage ◽  
Spherical Motion

The subject of this paper is the formulation of a specific algorithm for the kinematic analysis of spherical four-bar linkages via the inflection spherical cubic and spherical Thales ellipse by devoting particular attention to the crossed four-bar linkage (anti-parallelogram). Moreover, both the inflection and the elliptic cones, which represent the equivalent of the Bresse cylinders of the planar case in three-dimensions, are obtained by showing the particular properties of the spherical motion in terms of the curvature of a coupler curve and both the velocity and acceleration vector fields. Of special interest are also the cases in which the three acceleration poles coincide at one unique point or in two plus one, which depends on the intersections of two spherical curves of third and second degree.

Leg kinematic analysis and prototype experiments of walking-operating multifunctional hexapod robot

2013 ◽  
Vol 228 (12) ◽  
pp. 2217-2232 ◽  
Author(s):  
Pan Yang ◽  
Feng Gao
Keyword(s):  
Kinematic Analysis ◽  
Kinematic Model ◽  
Form Solution ◽  
Spherical Joint ◽  
Universal Joint ◽  
Step Size ◽  
Work Space ◽  
Prismatic Joint ◽  
Forward Kinematic ◽  
Close Form

This paper presents kinematic analysis of a 3-degree of freedom parallel mechanism for hexapod walking-operating multifuctional robot. Each leg of the robot consists of three limbs: universal joint – prismatic joint chain (1-UP) and universal joint – prismatic joint – spherical joint chain (2-UPS) and at the end of the leg there is passive spherical joint to adjust to the uneven ground. In this paper, first the forward kinematic model is built and it shows that the model has close-form solution. Then the work space is discussed in which the robot feet trajectories can be projected. It can be shown that the current trajectories of the feet only take very small work space. After that force analysis is performed and the results show that the payload capability of the mechanism is very high. Experiments of the prototype show that the robot can walk easily with more than 150 kg loads while the step size is more than 0.5 m.

The Opposite Pole Quadrilateral as a Compatibility Linkage for Parameterizing the Center Point Curve

1993 ◽  
Vol 115 (2) ◽  
pp. 332-336 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Complex Number ◽  
Kinematic Analysis ◽  
Special Form ◽  
Body Form ◽  
Kinematic Theory ◽  
Opposite Pole ◽  
Center Point ◽  
Point Curve ◽  
Position Problem ◽  
Four Bar Linkage

In planar four-position kinematics, the centers of circles containing four positions of a point in a moving rigid body form the center point curve. This curve can be parameterized by analyzing a “compatibility linkage” obtained from a complex number formulation of the four-position problem. In this paper, we present another derivation of the center point curve using a special form of dual quaternions and the fact that it is identical to the pole curve. The defining properties of the pole curve lead to a parameterization by kinematic analysis of the opposite pole quadrilateral as a four-bar linkage. Thus the opposite pole quadrilateral becomes the compatibility linkage. This derivation generalizes to provide parameterizations for the center point cone of spherical kinematics and the central axis congruence of spatial kinematic theory.

Optimum Design and Trafficability Analysis for an Articulated Wheel-legged Forestry Chassis

2021 ◽  
pp. 1-17
Author(s):  
Zhibo Sun ◽  
Dan Zhang ◽  
Zhilong Li ◽  
Shi Yan ◽  
Na Wang
Keyword(s):  
Parameter Optimization ◽  
Kinematic Analysis ◽  
Screw Theory ◽  
Kinematic Model ◽  
Surface Profile ◽  
Error Rates ◽  
Wheel Slip ◽  
Working Environments ◽  
Rigid Model ◽  
Four Bar Linkage

Abstract High trafficability and stability are the most two significant features of the forestry chassis. In this study, in order to improve surface trafficability, a novel articulated wheel-legged forestry chassis(AWLFC) is presented. To balance the trafficability and stability, a serial suspension system which is a combination with the active four-bar linkage articulated suspension (AFLAS) and passive V shape rocker-bogie is proposed. Then, parameter optimization with a comprehensive object function is implemented not only to enhance the trafficability and stability benefit of the structure but also to reduce the wheel slip. After that, through the flexible kinematic model based on screw theory, characteristics such as leveling ability and surface profile accessibility of the chassis are analyzed. The minimum accessible radius is obtained as 3088mm, and the longitudinal and lateral leveling angle reaches to 22° and 28.7° separately. The new chassis performs better on leveling ability and surface profile accessibility than the forestry chassis in the current literature. Finally, compared with the simulation and prototype experiment, error rates of the flexible kinematic analysis are reduced by 12.2% and 8.6% related to the rigid model. Previously inaccessible forestry working environments can be available with the development of AWLFC.

scholarly journals The Coupler Surface of the RSRS Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Nicolas Rojas ◽  
Aaron M. Dollar
Keyword(s):  
Rigid Body ◽  
Interested Reader ◽  
Implicit Equation ◽  
Spatial Mechanism ◽  
Full Equation ◽  
Sextic Curve ◽  
Spatial Linkages ◽  
Robotic Devices ◽  
Four Bar Linkage ◽  
Two Degree Of Freedom

Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolute-spherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics study of this basic linkage has unexpectedly received little attention in the literature over the years. Counteracting this historical tendency, this work presents the derivation of the general implicit equation of the surface generated by a point on the coupler link of the general RSRS spatial mechanism. Since the derived surface equation expresses the Cartesian coordinates of the coupler point as a function only of known geometric parameters of the linkage, the equation can be useful, for instance, in the process of synthesizing new devices. The steps for generating the coupler surface, which is computed from a distance-based parametrization of the mechanism and is algebraic of order twelve, are detailed and a web link where the interested reader can download the full equation for further study is provided. It is also shown how the celebrated sextic curve of the planar four-bar linkage is obtained from this RSRS dodecic.

The Principle of a Three-DOF Mechanism for Wave Energy Absorption

2016 ◽  
Author(s):  
Weixing Chen ◽  
Xiangdun Meng ◽  
Feng Gao
Keyword(s):  
Wave Energy ◽  
Power Output ◽  
Wave Power ◽  
Spherical Joint ◽  
Hydraulic Power ◽  
Wave Energy Converters ◽  
Major Class ◽  
Absorption Performance ◽  
Heave Motion ◽  
Four Bar Linkage

As we all know, oceans have great wave power, and many types of wave energy converters (WECs) have been invented so far. Oscillating body systems are a major class of WECs which almost only have one degree of freedom (DOF). This paper presents a three-DOF mechanism which can extract the wave power from any wave directions. The three-DOF mechanism mainly consists of a four-bar linkage and a spherical joint, which are used to capture the heave motion and the pitch and roll motions of the oscillating body respectively. The power conversion principle of the WEC is proposed and the kinematics of the mechanism is derived. Hydraulic power take-off (PTO) systems are used, which are simplified as constant torques in this study. In the end, the power absorption performance of the WEC is presented based on the system dynamics. The results show that the rated power output of the WEC is 4.3MW, and the power output of the WEC is dependent on the wave directions.

Kinematic Analysis of Rectangular Path Generating Adjustable Four-Bar Linkage

2014 ◽  
Vol 592-594 ◽  
pp. 1094-1098 ◽  
Author(s):  
G. Ganesan ◽  
M. Sekar
Keyword(s):  
Angular Velocity ◽  
Kinematic Analysis ◽  
Kinematic Parameters ◽  
Transmission Angle ◽  
Adjustable Mechanism ◽  
Velocity Variations ◽  
Four Bar Linkage

This paper focuses on the kinematic analysis of rectangular path generating adjustable four-bar crank rocker linkage. One of the ground pivots of rocker side of the adjustable mechanism is subjected to continuous adjustment while the crank arm is given uniform angular velocity. Variations of coupler and rocker position, velocity and acceleration are computed for continuously changing phases of the adjustable four bar linkage. These kinematic parameters are compared with non-adjustable four-bar mechanism. Effect of the continuous adjustment on transmission angle and torque ratio are presented. The above procedures are implemented successfully in MATLAB environment and graphical results are presented.

An Equivalent Linkage Model for Understanding Stiffness Effects of Biarticular Muscles

2001 ◽  
Author(s):  
Donald L. Russell ◽  
Chad E. English
Keyword(s):  
Kinematic Analysis ◽  
Mechanical Model ◽  
Mechanical Analog ◽  
Biarticular Muscles ◽  
Human Arm ◽  
Four Bar Linkage ◽  
Linkage Model

Abstract The purpose of this paper is to describe a method for aiding in the intuitive understanding of the effects of bi-articular muscles on the stiffness of a limb. In particular, a kinematic analysis of a mechanical model of a human arm is performed. The results are manipulated into a form that makes evident a mathematical decomposition of the kinematics. This gives rise to a mechanical analog to the decomposition: an equivalent four-bar linkage with single-joint muscles. Further insight is gained as the equivalent linkage provides an intuitive direction associated with each set of muscles.

Approximate Synthesis of Spatial Linkages

1960 ◽  
Vol 27 (1) ◽  
pp. 201-206 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Helical Motion ◽  
Second Variation ◽  
Variable Pitch ◽  
Approximate Synthesis ◽  
Spatial Linkages ◽  
Four Bar Linkage

Freudenstein’s approximate synthesis of planar four-bar linkages is generalized to spatial linkages, and the conditions under which this generalization is applicable are expressed. Three cases of synthesis of spatial linkages to generate functions of one variable between nonparallel axes are considered in detail: (a) The spherical four-bar linkage; (b) a variation of the four-bar linkage in which two turning pairs are replaced by ball-and-socket joints, a linkage which may be designed to generate arbitrary functions with up to seven accuracy points; and (c) a second variation of the four-bar linkage where three turning pairs are replaced by cylinder pairs, a linkage capable of being designed to generate a variable-pitch helical motion with three accuracy points.

A Dual Number Approach to the Kinematic Analysis of Spatial Linkages With Dimensional and Geometric Tolerances

2004 ◽  
Author(s):  
Emanuele Cecchini ◽  
Ettore Pennestri` ◽  
Roberto Stefanelli ◽  
Leonardo Vita
Keyword(s):  
Kinematic Analysis ◽  
Tolerance Analysis ◽  
Rigid Bodies ◽  
Kinematic Modeling ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis ◽  
Spatial Linkages ◽  
Joint Clearances ◽  
First Time ◽  
Cardan Joint

Design robustness is somewhat connected to tolerances. In fact, the lower is the sensitivity of the kinematic function to the deviations of manufacturing process, the higher is the robustness of the design. In this investigation is described a tolerance analysis method based on dual vectors kinematic modeling of spatial linkages and on Monte Carlo simulation of the random variables. In the present analysis the hypothesis of rigid bodies is valid and only kinematic variables are considered in output. The method is applied to a Cardan joint modelled as an RCCC linkage with main dimensions considered as stochastic variables with Gaussian distribution. Dual vectors are well known in kinematic analysis and synthesis of spatial mechanisms. When compared with traditional vectorial methods, dual vectors show an enhanced capability to model misalignments among kinematic pairs axes. Although this is not the first time that dual vectors are used for the kinematic and dynamic analysis of spatial mechanisms with manufacturing errors, the present use of dual vectors to model joint clearances seems somewhat novel.

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