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.

Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Aravind Baskar ◽  
Mark Plecnik
Keyword(s):  
Rigid Body ◽  
Complete Solution ◽  
Numerical Algebraic Geometry ◽  
Algebraic Equations ◽  
Solution Sets ◽  
Root Finding ◽  
Rigid Body Motions ◽  
Joint Variable ◽  
Four Bar Linkage ◽  
Parameter Continuation

Abstract Synthesis of rigid-body mechanisms has traditionally been motivated by the design for kinematic requirements such as rigid-body motions, paths, or functions. A blend of the latter two leads to timed curve synthesis, the goal of which is to produce a path coordinated to the input of a joint variable. This approach has utility for altering the transmission of forces and velocities from an input joint onto an output point path. The design of timed curve generators can be accomplished by setting up a square system of algebraic equations and obtaining all isolated solutions. For a four-bar linkage, obtaining these solutions is routine. The situation becomes much more complicated for the six-bar linkages, but the range of possible output motions is more diverse. The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry. In particular, we implement a method that uses random monodromy loops. In this work, we report these solution sets to all relevant six-bars of the Stephenson topology. The computed solution sets to these generic problems represent a design library, which can be used in a parameter continuation step to design linkages for different subsequent requirements.

The Optimization of Dimensions of an Adjustable Mechanism for a Packaging Machine

1989 ◽  
Vol 203 (1) ◽  
pp. 37-40 ◽  
Author(s):  
A Daadbin ◽  
K S H Sadek
Keyword(s):  
Rigid Body ◽  
Complex Mechanism ◽  
Uniform Velocity ◽  
Packaging Machine ◽  
Minimum Number ◽  
Adjustable Mechanism ◽  
Spatial Linkages ◽  
Mechanical Devices ◽  
Cam Systems

Mechanisms form the basic geometrical elements of many mechanical devices including automatic packaging machinery, typewriters, textile and printing machinery, and others. A mechanism typically is designed to create a desired motion of a rigid body relative to a reference member by the help of gears, cam systems or spatial linkages. In flow pack machines a tube of wrapper containing the products moves with a uniform velocity, while the reciprocating heads move forward and backwards sealing different products. In an existing machine, these motions are produced by a rather complex mechanism involving cams and adjustable links. The paper suggests replacing these cams by a suitable quick-return mechanism with a minimum number of adjustable links. The dimensions of this mechanism are optimized such that the motions produced are as near as possible to those obtained by the original cam mechanisms. The simplification can result in reduction in the mass of different components and existing forces in the mechanism.

Identifying the Shapes of Coupled Vibrations and Deriving Reduced Order Models for Nonlinear Shafts: A Finite Element-Proper Orthogonal Decomposition Approach

2004 ◽  
Author(s):  
I. T. Georgiou ◽  
M. A. Bani-Khaled
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Rotating Shaft ◽  
Decomposition Approach ◽  
Reduced Order ◽  
Coupled Vibrations ◽  
Orthogonal Decompositions ◽  
Proper Orthogonal Decompositions ◽  
Proper Orthogonal ◽  
Two Degree Of Freedom

The spatial structure of the dynamics of a rotating nonlinear shaft is identified by processing its finite element dynamics by the method of Proper Orthogonal Decompositions. The Proper Orthogonal modes furnish characteristic signatures for the rigid body and the whirling modes of a motion. The pattern of energy distribution over the components of a mode reveals the strength of coupling between rigid body rotations and coupled vibrations. These modes are used to derive a two-degree-of freedom reduced model for the whirling motion of the rotating shaft.

Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis

1973 ◽  
Vol 95 (2) ◽  
pp. 603-611 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Bernard Roth
Keyword(s):  
Rigid Body ◽  
Screw Axis ◽  
Numerical Examples ◽  
Spatial Linkages ◽  
Free Parameters ◽  
Analytical Expressions ◽  
Linkage Synthesis

The screw axis geometry associated with displacements of points and lines is studied. Analytical expressions are developed for rigid body screw displacements which have one or more free parameters. It is shown how to apply these results to the synthesis of spatial linkages. The theory is illustrated by numerical examples in which Cylindric-Cylindric cranks are designed to guide two points in a rigid body through five and then nine specified positions.

An Under-Actuated 5-DOF Robotic Manipulator for Ultrasound Transducer Guidance Using a Passive Four-Bar Linkage

2009 ◽  
Author(s):  
Allan R. Provorse ◽  
Carl A. Nelson ◽  
Gregory R. Bashford ◽  
Judith M. Burnfield ◽  
Kornelia Kulig
Keyword(s):  
Achilles Tendon ◽  
Medical Practice ◽  
Robotic Manipulator ◽  
Response To Treatment ◽  
Robot Kinematics ◽  
Ultrasound Transducer ◽  
Ultrasound Probe ◽  
The Subject ◽  
Robotic Devices ◽  
Four Bar Linkage

Robotic devices have made inroads in various areas of medical practice. This paper offers a design of robot kinematics for ultrasound probe manipulation to obtain reproducible Achilles tendon images for quantifying injury or response to treatment. The design includes a motor-controlled 4-DOF arm with an additional smaller, passive four-bar linkage mount for the ultrasound probe to optimize surface contact with the subject and increase the mobility to 5 DOF.

Software for the Kinematic Synthesis of Coupler-Driven Spherical Four-Bar Mechanisms

2007 ◽  
Author(s):  
Eric M. Grimm ◽  
Andrew P. Murray ◽  
Michael L. Turner
Keyword(s):  
Rigid Body ◽  
Kinematic Synthesis ◽  
Prismatic Joint ◽  
Second Stage ◽  
Typical Scheme ◽  
Four Bar Linkage

A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force applied directly to the coupler. This linkage is termed the coupler-driven spherical four-bar mechanism, and defines an alternative to the typical scheme of actuating the four-bar via a torque applied at the input link. This paper presents software developed to assist in the kinematic synthesis of these mechanisms. In the first stage of the design, a circuit-defect free spherical four-bar is dimensioned with the capacity to guide a rigid body through two orientations. The second stage of the design is to locate the SPS leg such that the four-bar is smoothly drivable between the orientations.

Study of Forward Connecting Rod Combined Lifting Mechanism Based on Linear Transformation and Vector Algebra

2012 ◽  
Vol 155-156 ◽  
pp. 505-508
Author(s):  
Ming Qing Wu
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Linear Transformation ◽  
Plane Motion ◽  
Connecting Rod ◽  
Vector Algebra ◽  
Lift Mechanism ◽  
Four Bar Linkage ◽  
The Mathematical Model

By adopting the method of block analysis,the paper analyzes and calculates the forward connecting rod combined lift mechanism by broking up it into a four-bar linkage and the plane motion of an arm triangle rigid body, constructs the kinematic equations of four-bar linkage and arm triangle and the static equations of four-bar linkage based on linear transformation and vector algebra and establishes the mathematical model of lift mechanism based on linear transformation and vector algebra.

The Synthesis of Spherical Motion Generators in the Presence of an Incomplete Set of Attitudes

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Khalid Al-Widyan ◽  
Jorge Angeles
Keyword(s):  
Rigid Body ◽  
Engineering Design ◽  
Theoretical Framework ◽  
General Methodology ◽  
Four Bar Linkage ◽  
Robust Engineering Design ◽  
Guidance Problem ◽  
Spherical Motion ◽  
Spherical Rigid Body ◽  
Selection Of

Proposed in this paper is a general methodology applicable to the synthesis of spherical motion generators in the presence of an incomplete set of finitely separated attitudes. The spherical rigid-body guidance problem in the realm of four-bar linkage synthesis can be solved exactly for up to five prescribed attitudes of the coupler link, and hence, any number of attitudes smaller than five is considered incomplete in this paper. The attitudes completing the set are determined to produce a linkage whose performance is robust against variations in the unprescribed attitudes. Robustness is needed in this context to overcome the presence of uncertainty due to the selection of the unspecified attitudes, that many a time are specified implicitly by the designer upon choosing, for example, the location of the fixed joints of the dyads. A theoretical framework for model-based robust engineering design is thus, recalled, and a methodology for the robust synthesis of spherical four-bar linkages is laid down. An example is included here to concretize the concepts and illustrate the application of the proposed methodology.

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

Sign in / Sign up

Export Citation Format

Share Document