Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

A New Family of Deployable Mechanisms Derived From Two-Layer and Two-Loop Spatial Linkages With Five Revolute Pair Coupling Chains

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Wen-ao Cao ◽  
Donghao Yang ◽  
Huafeng Ding
Keyword(s):  
Structural Characteristics ◽  
Degree Of Freedom ◽  
Single Loop ◽  
New Family ◽  
Serial Chain ◽  
Spatial Linkages ◽  
Application Requirements ◽  
Pair Coupling

This paper aims to construct a novel family of deployable mechanisms from a class of two-layer and two-loop spatial linkages, each of which consists of an eight revolute pair (8R) single-loop linkage connected by a 5R serial chain. First, structural characteristics of the class of linkages as deployable units are analyzed and illustrated. Then, the two-layer and two-loop spatial linkages with 5R chains satisfying the structural characteristics are systematically synthesized. Mobile assembly modes between deployable units are established based on degree-of-freedom (DOF) analysis. Finally, a family of single DOF deployable mechanisms is constructed based on the synthesized deployable units and the established assembly modes. The derived deployable mechanisms have the characteristic of the umbrella-like structure, and they have various mesh shapes, which can meet different kinds of application requirements.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1994 ◽  
Vol 116 (2) ◽  
pp. 614-621 ◽  
Author(s):  
Yong-Xian Xu ◽  
D. Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

scholarly journals Residue-Residue Mutual Work Analysis of Retinal-Opsin Interaction in Rhodopsin: Implications for Protein-Ligand Binding

2019 ◽  
Author(s):  
Wenjin Li
Keyword(s):  
Virtual Work ◽  
Interaction Matrix ◽  
Time Interval ◽  
Transition Path ◽  
Transition Path Sampling ◽  
Decomposition Approach ◽  
Work Analysis ◽  
Nmr Study ◽  
The Matrix ◽  
Dynamics Simulations

AbstractEnergetic contributions at single-residue level to retinal-opsin interaction in rhodopsin were studied by combining molecular dynamics simulations, transition path sampling, and a newly developed energy decomposition approach. The virtual work at an infinitesimal time interval was decomposed into the work components on one residue due to its interaction with another residue, which were then averaged over the transition path ensemble along a proposed reaction coordinate. Such residue-residue mutual work analysis on 62 residues within the active center of rhodopsin resulted in a very sparse interaction matrix, which is generally not symmetric but anti-symmetric to some extent. 14 residues were identified to be major players in retinal relaxation, which is in excellent agreement with an existing NMR study. Based on the matrix of mutual work, a comprehensive network was constructed to provide detailed insights into the chromophore-protein interaction from a viewpoint of energy flow.

A Proposed Categorization Method and Category Domain Inequality Development Procedure for Ground Joints of Five Bar Linkages

1998 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Terry Lee ◽  
Bao-Ping Jia
Keyword(s):  
Computer Program ◽  
Single Loop ◽  
Loop Equation ◽  
Development Procedure ◽  
Five Dimension ◽  
Simple Logic ◽  
Logic Operations ◽  
Definition Of ◽  
Dimension Space ◽  
The Given

Abstract This paper presents a method for the development of sets of symbolic inequalities in terms of link lengths for the prediction of the rotation capabilities of ground joints of single-loop five-bar linkages. The inequalities are obtained from the combination of the loop equation of a five-bar linkage and its derivatives and the application of simple logic operations. The rotation capabilities of ground joints are divided into three categories: the incomplete-rotation ground joints, the conditioned complete-rotation ground joints, and the unconditioned complete-rotation ground joints. The derived sets of inequalities define the domain, in a five-dimension space of the five link lengths, for each of the rotation categories. In this paper, the definition of each category is clearly described and the derivations of sets of inequalities are explained in details. A computer program was constructed to examine the completeness and correctness of the categorization method and to analyze the given five-bar linkages to determine the appropriate categories for their ground joints.

scholarly journals Reconfiguration Analysis of an RRRRS Single-Loop Mechanism

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 51
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Numerical Solutions ◽  
Motion Equation ◽  
Degree Of Freedom ◽  
Solid Model ◽  
Variable Degree ◽  
Single Loop ◽  
Motion Modes ◽  
The One ◽  
Classical Vector ◽  
First Time

The paper deals with the reconfiguration analysis of the single-loop variable degree-of-freedom (DOF) RRRRS mechanism composed of five links connected by four revolute (R) joints and one spherical (S) joint. The mechanism may show two modes of motion: one-DOF and two-DOF motion. In the paper, a classical vector procedure is used to obtain the quartic motion equation (QME) that allows one to inspect the nature of the motion. In general, the solutions of the QME provide the one-DOF motion of the mechanism except when all the coefficients of the equation vanish. In this case, the mechanism undergoes the two-DOF motion. The motion of the mechanism built according to two specific architectures was analyzed by the numerical solutions of the QME and with the help of the solid model of the mechanism. It is revealed for the first time that the perpendicular architecture has one 2-DOF motion and two 1-DOF motion modes.

scholarly journals Dynamics analysis and electromagnetic characteristics calculation of permanent magnet 3-degree-of-freedom motor

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041987421
Author(s):  
Zheng Li ◽  
Lingqi Liu
Keyword(s):  
Permanent Magnet ◽  
High Speed ◽  
Permanent Magnets ◽  
Control Strategies ◽  
Core Loss ◽  
Degree Of Freedom ◽  
Theoretical Formula ◽  
Virtual Displacement ◽  
High Speed Rotation ◽  
Actual Operation

This article proposes a conceptual model of a new type permanent magnet 3-degree-of-freedom motor. Its structure consists of an internal rotation module and a peripheral deflection module. It can be driven independently to achieve high-speed rotation and precise tilting of the motor. The 3-degree-of-freedom movement of the motor in space is achieved by the synchronous operation of the rotation and the deflection. In order to explore the loss problem caused by the temperature rise problem in the actual operation of the motor, the eddy current loss and core loss inside the permanent magnet of the motor are analyzed by theoretical formula and finite element method, respectively. Based on the static magnetic field, the gas flux density of two types of rotor permanent magnets in different coordinate systems is analyzed. The motor’s rotation and deflection torque characteristics are calculated using the principle of virtual displacement method. Using the auxiliary technology of the virtual prototype, according to the actual situation of the motor, the corresponding motion hinges and driving forms are summarized, and the control strategies of rotation, deflection, and rotation and deflection simultaneously are planned. The trajectory of the motor is described by observing the selected points. For the motor from product design to prototype testing and to the final processing assembly, a solid theoretical foundation is laid for the proposed work.

scholarly journals An Algebraic Method on the Eigenvalues and Stability of Delayed Reaction-Diffusion Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jian Ma ◽  
Baodong Zheng
Keyword(s):  
Asymptotic Stability ◽  
Linear Operator ◽  
Reaction Diffusion ◽  
Matrix Pencil ◽  
Algebraic Method ◽  
Delayed Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
The Matrix ◽  
Pure Imaginary Eigenvalues

The eigenvalues and stability of the delayed reaction-diffusion systems are considered using the algebraic methods. Firstly, new algebraic criteria to determine the pure imaginary eigenvalues are derived by applying the matrix pencil and the linear operator methods. Secondly, a practical checkable criteria for the asymptotic stability are introduced.

Rigid Foldability of Triangle-Twist Origami Pattern and its Derived 6R Linkage

2017 ◽  
Author(s):  
Rui Peng ◽  
Jiayao Ma ◽  
Yan Chen
Keyword(s):  
Theoretical Method ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Space Structures ◽  
Engineering Applications ◽  
Systematic Method ◽  
Mountain Valley ◽  
Folding Pattern ◽  
Spatial Linkages ◽  
Spherical Linkages

Rigid origami is an important subset of origami with broad engineering applications from space structures to metamaterials. The rigid foldability of an origami pattern is determined by both the geometric parameters and the mountain-valley crease assignment. In this paper, by using the equivalent relationships between origami vertices and spherical linkages, a systematic method was proposed to analyze the motion of the triangle-twist pattern with varying distribution of mountain and valley creases, and its rigid folding types were identified. Moreover, kirigami technology was applied to the rigid folding pattern without changing its degree of freedom, from which a new kind of overconstrained 6R linkage was developed. The theoretical method proposed in this paper can be readily extended to study other types of origami patterns, which will in turn help to design structures with large deployable ratio as well as some new spatial linkages.

Synthesizing Single DOF Linkages Via Transition Linkage Identification

2007 ◽  
Vol 130 (2) ◽  
Author(s):  
Andrew P. Murray ◽  
Michael L. Turner ◽  
David T. Martin
Keyword(s):  
Classification Scheme ◽  
Degree Of Freedom ◽  
Physical Parameters ◽  
Single Degree Of Freedom ◽  
Loop Closure ◽  
Single Degree ◽  
The Matrix ◽  
Comprehensive Classification ◽  
Insight Into ◽  
Selection Of

A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the physical parameters that may alter this classification. The limits on the physical parameters that result in no change in the classification are defined by transition linkages. More rigorously, a transition linkage possesses a configuration at which the matrix defined by the derivative of the loop closure equations with respect to the joint variables loses rank. Transition linkages divide the set of all linkages into different classifications. In the simplest cases studied, transition linkage identification produces a comprehensive classification scheme. In all cases, this identification is used to alter a linkage’s physical parameters without changing its classification and produces insight into the selection of these parameters to produce a desired classification.

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