scholarly journals Four-Bar Linkage Synthesis for a Combination of Motion and Path-Point Generation

2013 ◽  
Author(s):  
Yuxuan Tong ◽  
David H. Myszka ◽  
Andrew P. Murray
Keyword(s):  
Numerical Solutions ◽  
Kinematic Chain ◽  
Object Motion ◽  
Synthesis Methods ◽  
Motion Generation ◽  
Range Of Movement ◽  
Pick And Place ◽  
Four Bar Linkage ◽  
Path Point ◽  
Linkage Synthesis

This paper develops techniques that address the design of planar four-bar linkages for tasks common to pick-and-place devices, used in assembly and manufacturing operations. Pick-and-place tasks often require the exact position and orientation of an object (motion generation) at the end points of the task. Within the range of movement, the motion restrictions are less rigorous with only the position of the object (path-point generation) being specified to avoid obstacles. Established synthesis theory has been developed for either motion generation or path-point generation tasks. This paper presents four-bar linkage synthesis methods for tasks that include a combination of motion and path requirements. This synthesis challenge is addressed via two approaches: Geometric Constraint Programming (GCP) and numerical solutions to synthesis equations. Using GCP, a step-by-step methodology has been established to find solutions to these synthesis challenges. Using numerical methods, techniques are presented to formulate kinematic chain constraint equations and solve for appropriate link lengths and pivot locations. Examples of various combinations of motion and path-point generation are presented.

Four-Bar Linkage Synthesis Methods for Two Precision Positions Combined With N Quasi-Positions

1995 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Synthesis Method ◽  
Synthesis Methods ◽  
Bounded Motion ◽  
Transmission Angle ◽  
Pass Through ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Exact Positions ◽  
Linkage Synthesis

Abstract Mechanisms seldom need to pass through more than one or two exact positions. The method of quasi-position synthesis combines a number of approximate or “quasi” positions with two exact positions to design four-bar linkages that will produce a specified, bounded motion. Quasi-position synthesis allows for the optimization of some linkage characteristic (such as link lengths or transmission angles) by using the three variables that describe a single quasi-position. Procedures for circuit and transmission angle rectification are also easily incorporated into the quasi-position synthesis method.

Planar Linkage Synthesis for Rigid Body Guidance Using Poles and Rotation Angles

2013 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Center Point ◽  
Circle Center ◽  
Previous Solution ◽  
Design Software ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

A graphical four bar linkage synthesis method for planar rigid body guidance is presented. This method, capable of synthesis for up to five specified coupler positions, uses the poles and rotation angles, which are constraints, to define guiding links. Faster and simpler than traditional graphical synthesis methods, this method, allows the designer to see and consider most or all the possible solutions within a few seconds before making any free choices. All of the guiding links satisfying five specified coupler positions can be obtained graphically within 30 minutes without plotting any Burmester curves and without any mechanism design software. For four positions, both the circle and center point curves are simultaneously traced by corresponding circle-center point pairs using three poles having a common subscript and the corresponding rotation angles without any additional construction. This method eliminates the iterative construction required in previous methods which were based on free choices rather than constraints. The tedious plotting of Burmester curves graphically using pole quadrilaterals is also eliminated. The simplicity of the method makes four and five position synthesis practical to do graphically. A corresponding analytical solution is presented which provides a simpler formulation than the previous solution method. This new method requires two fewer equations and provides a new way to plot Burmester curves analytically.

Synthesis and Balancing of Cam-Modulated Linkages

1987 ◽  
Author(s):  
P. Pracht ◽  
P. Minotti ◽  
M. Dahan
Keyword(s):  
Systematic Approach ◽  
Kinematic Chain ◽  
Path Generation ◽  
Industrial Manipulator ◽  
High Speeds ◽  
Structural Error ◽  
Mass Balancing ◽  
Four Bar Linkage ◽  
Robotic Applications ◽  
Class Of Functions

Abstract Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

scholarly journals Four-Bar Linkage Synthesis Using Non-convex Optimization

2016 ◽  
pp. 618-635 ◽  
Author(s):  
Vincent Goulet ◽  
Wei Li ◽  
Hyunmin Cheong ◽  
Francesco Iorio ◽  
Claude-Guy Quimper
Keyword(s):  
Convex Optimization ◽  
Four Bar Linkage ◽  
Linkage Synthesis

Linkage Synthesis of a Four-Bar Mechanism for N Precision Points Using Simulated Annealing

1998 ◽  
Author(s):  
Horacio Martínez-Alfaro ◽  
Homero Valdez ◽  
Jaime Ortega
Keyword(s):  
Simulated Annealing ◽  
Computational Intelligence ◽  
Simulated Annealing Algorithm ◽  
Alternative Synthesis ◽  
Computational Intelligence Technique ◽  
Annealing Algorithm ◽  
Four Bar Linkage ◽  
Generation Problem ◽  
Intelligence Technique ◽  
Linkage Synthesis

Abstract This paper presents an alternative way of linkage synthesis by using a computational intelligence technique: Simulated Annealing. The technique allows to define n precision points of a desired path to be followed by a four-bar linkage (path generation problem). The synthesis problem is transformed into an optimization one in order to use the Simulated Annealing algorithm. With this approach, a path can be better specified since the user will be able to provide more “samples” than the usual limited number of five allowed by the classical methods. Several examples are shown to demonstrate the advantages of this alternative synthesis technique.

Kinematics and Stiffness Modeling of a 4-DOF Parallel Robot for Schönflies Motion Generation

2014 ◽  
Author(s):  
Shaoping Bai ◽  
Lasse Køgs Andersen ◽  
Carsten Rebbe Mølgaard
Keyword(s):  
Dynamic Performance ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Motion Generation ◽  
Stiffness Modeling ◽  
Pick And Place ◽  
Fea Simulation ◽  
Schönflies Motion ◽  
Pick And Place Operation ◽  
Good Agreement

This work deals with the design of parallel robots for the generation of pick-and-place operation, or Schönflies motion. The aim is to develop a robot with workspace optimized for fast pick-and-place operations, namely, a robot with a superellipsoidal reachable volume, which suits best for the pick-and-place operations on conveyers, where robots’ working areas are nearly rectangular. In this paper, the kinematics and stiffness modeling of the new robot are presented. A method of stiffness modeling by means of Castigliano’s Theorem is developed. Using the new method, the stiffness of the robot is analyzed. The results are compared with FEA simulation, which shows a good agreement between the results. The method is finally applied to the engineering design of the new robot for enhanced static and dynamic performance.

Performance of EAs for four-bar linkage synthesis

2009 ◽  
Vol 44 (9) ◽  
pp. 1784-1794 ◽  
Author(s):  
S.K. Acharyya ◽  
M. Mandal
Keyword(s):  
Four Bar Linkage ◽  
Linkage Synthesis

Unifying model of carpal mechanics based on computationally derived isometric constraints and rules-based motion – the stable central column theory

2013 ◽  
Vol 39 (4) ◽  
pp. 353-363 ◽  
Author(s):  
M. J. Sandow ◽  
T. J. Fisher ◽  
C. Q. Howard ◽  
S. Papas
Keyword(s):  
Kinetic Theory ◽  
Three Dimensional ◽  
Normal Subjects ◽  
Range Of Movement ◽  
Lateral Column ◽  
Central Column ◽  
Three Dimensional Models ◽  
Carpal Mechanics ◽  
Forward Kinematic ◽  
Four Bar Linkage

This study was part of a larger project to develop a (kinetic) theory of carpal motion based on computationally derived isometric constraints. Three-dimensional models were created from computed tomography scans of the wrists of ten normal subjects and carpal spatial relationships at physiological motion extremes were assessed. Specific points on the surface of the various carpal bones and the radius that remained isometric through range of movement were identified. Analysis of the isometric constraints and intercarpal motion suggests that the carpus functions as a stable central column (lunate–capitate–hamate–trapezoid–trapezium) with a supporting lateral column (scaphoid), which behaves as a ‘two gear four bar linkage’. The triquetrum functions as an ulnar translation restraint, as well as controlling lunate flexion. The ‘trapezoid’-shaped trapezoid places the trapezium anterior to the transverse plane of the radius and ulna, and thus rotates the principal axis of the central column to correspond to that used in the ‘dart thrower’s motion’. This study presents a forward kinematic analysis of the carpus that provides the basis for the development of a unifying kinetic theory of wrist motion based on isometric constraints and rules-based motion.

Synthesis and Analysis of a Chebyschev’s Straight Line Four-Bar Linkage for Generating a Minimum Jerk Velocity Profile

2014 ◽  
Author(s):  
Evagoras G. Xydas
Keyword(s):  
Velocity Profile ◽  
Kinematic Chain ◽  
Mechanical Constraints ◽  
Minimum Jerk ◽  
Straight Line ◽  
Wide Range ◽  
Spatio Temporal ◽  
Line Trajectory ◽  
Four Bar Linkage ◽  
Input Torque

The interaction between human and passive, constraint-based path generating mechanisms has been scarcely studied. When it comes to rehabilitation robots, output trajectories and/or forces are achieved mainly as a result of actuation on all joints, since they form an open kinematic chain. On the other end, there exists a wide range of mechanisms that can trace complex trajectories primarily due to mechanical constraints in their topology and structure. Probably the simplest example is the four bar linkage, a widely used 1-DOF mechanism. It consists of a driving link, a driven link, and a coupler which connects the two. As the input link rotates, each point on the coupler link traces a unique trajectory in space, called a coupler curve. Ideally, the linkage dimensions can be chosen so that a near-natural hand trajectory is generated for a specific task. As a first step, in this work a straight line generating four-bar mechanism, namely the Chebyshev’s linkage is considered for generating a natural bell-shaped velocity profile, as prescribed by the Minimum-Jerk-Model. Initially the mechanism is synthesized for producing a straight line trajectory of a desired length. Kinematic and kinetostatic analysis is performed in order to determine the required input torque necessary for achieving the desired spatio-temporal profile. The main objective is to determine whether this input torque can approximated by a series of linear torsional springs that can be installed on the pivoted side of the input link.

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