A Simple Analytical Method for Teaching Force Analysis of Planar Frictionless Mechanisms

2005 ◽  
Author(s):  
Kazem Abhary
Keyword(s):  
Algebraic Equation ◽  
Analytical Method ◽  
Kinematic Analysis ◽  
Simultaneous Equations ◽  
Degree Of Freedom ◽  
Force Analysis ◽  
Equilibrium Equations ◽  
Planar Mechanisms ◽  
Joint Force ◽  
Teaching Force

A purely analytical method for teaching force analysis of one degree-of-freedom planar frictionless mechanisms has been developed herein. The method uses the vectorial illustration of mechanisms, which is widely used for kinematic analysis of mechanisms too. In this method, a joint-force is determined either via its decomposition into the direction of its adjacent links or from the equilibrium equations of one of these links. Unlike the conventional analytical method which leads to a system of simultaneous equations, this method leads to only one simple algebraic-equation or one simple vectorial-equation at a time. Force analysis of planar mechanisms has always been tedious and time consuming but this method has proved to be simple, straightforward and quick. It is therefore a most suitable tool for teaching mechanisms as it downgrades the project-type problems to the level of classroom tutorials.

Fixture Clamping Force Analysis during Milling Process

2013 ◽  
Vol 278-280 ◽  
pp. 385-388 ◽  
Author(s):  
Shao Gang Liu ◽  
Qiu Jin
Keyword(s):  
Analytical Method ◽  
Linear Equations ◽  
Milling Process ◽  
Contact Forces ◽  
Clamping Force ◽  
Contact Deformation ◽  
Force Analysis ◽  
Equilibrium Equations ◽  
Tangential Contact ◽  
Fixture Element

This paper presents a analytical method to calculate the minimum clamping force to prevent slippage between the workpiece and spherical-tipped fixture elements during milling process. After the contact deformation between the workpiece and spherical-tipped fixture element is determined, the relationships between the workpiece displacement and the contact deformations are obtained. Based on the static equilibrium equations, these equations are combined and linear equations are obtained to calculate the tangential contact forces between the workpiece and spherical-tipped fixture element. According to the maximum tangential contact force, the minimum clamping force to prevent slippage between the workpiece and spherical-tipped fixture elements is calculated. At last, this method is illustrated with a simulation example.

A Generalized Approach for the Kinematic Analysis of Planar Mechanisms

1995 ◽  
Vol 209 (4) ◽  
pp. 237-244
Author(s):  
D J A Simpson ◽  
J E L Simmons ◽  
G Moldovean
Keyword(s):  
Computer Program ◽  
Analytical Method ◽  
Building Block ◽  
Kinematic Analysis ◽  
Displacement Velocity ◽  
Planar Mechanisms ◽  
New Approach ◽  
Wide Range ◽  
Complex Mechanisms

This paper describes a new approach to the kinematic analysis of planar mechanisms. The basis of the analytical method is a generic four-bar sub-mechanism which is used as the single building block from which other composite mechanisms may be created. A computer program has been written embodying this method and has been demonstrated to operate successfully providing animated displays of displacement, velocity and acceleration diagrams for a wide range of complex mechanisms.

Analysis of Circular Braiding Process, Part 2: Mechanics Analysis of the Circular Braiding Process and Experiment

1999 ◽  
Vol 121 (3) ◽  
pp. 351-359 ◽  
Author(s):  
Q. Zhang ◽  
D. Beale ◽  
R. M. Broughton ◽  
S. Adanur
Keyword(s):  
Algebraic Equation ◽  
Kinematic Analysis ◽  
Equilibrium Equations ◽  
Friction Forces ◽  
Final Structure ◽  
Mechanics Model ◽  
Mechanics Analysis ◽  
Newton Raphson ◽  
Braided Structure ◽  
Raphson Method

The final structure of a braid is a consequence of force interactions among yarns in the convergent zone. In Part 1, the influence of friction forces on the final braided structure was discussed via kinematic analysis. A transformation from a 3-D cone to a 2-D plane was made for the mechanics analysis. A mechanics model is proposed in this paper to determine the braid angle by considering interlacing forces. Equilibrium equations for the braiding process are deduced. A Newton-Raphson method is used to solve the nonlinear algebraic equation set. Experiments have been conducted to produce braids at different machine speeds and with different tensions, and reveal that the mechanics model is potentially a better predictor of final braid structure than the kinematic analysis.

Kinetic Analysis of Planar Frictionless Mechanisms Made Simple

2003 ◽  
Author(s):  
Kazem Abhary
Keyword(s):  
Kinetic Analysis ◽  
Analytical Method ◽  
Simultaneous Equations ◽  
Graphical Methods ◽  
Planar Mechanisms ◽  
Conservation Of Energy ◽  
Teaching Technique ◽  
Kinetic Force ◽  
Force Equilibrium

A purely analytical method has been developed for the kinetic (force or kinetostatic) analysis of frictionless planar mechanisms. It employs polar notation of vectors, the principle of conservation of energy and the force equilibrium of the links. Unlike many other methods which lead to a system of several simultaneous equations, it leads to only one algebraic or one vectorial equation at a time and, interestingly, it is less time consuming that the conventional graphical methods. The method is general, comprehensive and systematic such that it could also serve as a suitable teaching technique for manual approach to the problem. It easily lends itself to automation too.

Design of Hybrid-Driven Servo Press Mechanism

2005 ◽  
Author(s):  
Pei-Lum Tso ◽  
Cheng-Ho Li ◽  
Jyun-Huang Ke
Keyword(s):  
Analytical Method ◽  
Kinematic Analysis ◽  
Degree Of Freedom ◽  
Significant Benefit ◽  
Constant Speed ◽  
Dimensional Synthesis ◽  
Normal Constant ◽  
Motion Function ◽  
Servo Press ◽  
The Press

Servo presses are notably developed and studied nowadays out of their flexible ram motion. In practice, press users can advantageously utilize a single servo press to deal with different stamping operations such as blanking, drawing, coining, embossing, etc. In this paper, a hybrid-driven servo press mechanism is studied. The mechanism for such servo presses is a seven-bar linkage whose degree of freedom (DOF) is “2”. Two input links of the press mechanism are driven by one normal constant-speed motor and one servo variant-speed motor respectively. The dimensional synthesis of the press mechanism that is based on an analytical method is proposed. The motion function of the servomotor that generated a specified ram motion is derived by kinematic analysis. A design example is illustrated, and it shows that one could apply the proposed method to design a hybrid-driven press mechanism capable of carrying out various ram motions. This work contributes to press mechanism designers a method of dimensional synthesis. The ram motion flexibility of the servo press is achieved, and this provides significant benefit to improve the performance of any different kind of stamping operations.

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Analytical Method ◽  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Graphical Method ◽  
Degree Of Freedom ◽  
Workspace Analysis ◽  
Fixed Base ◽  
Moving Platform

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

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.

scholarly journals Torque modeling and characteristic analysis of electromagnetic piezoelectric hybrid-driven 3-degree-of-freedom motor

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880474 ◽  
Author(s):  
Zheng Li ◽  
Peng Guo ◽  
Ruihua Han ◽  
Qunjing Wang
Keyword(s):  
Analytical Method ◽  
Optimization Design ◽  
Basic Structure ◽  
Position Angle ◽  
Degree Of Freedom ◽  
Hybrid Drive ◽  
Characteristic Analysis ◽  
Drive Motor ◽  
And Performance ◽  
Air Gap Magnetic Field

The electromagnetic piezoelectric hybrid-driven 3-degree-of-freedom motor is a new multi-degree-of-freedom motor. To further analyze the torque characteristics of the electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor. First, the principle and basic structure of the hybrid-drive motor are introduced, and the displacement and pressure distribution of the stator–rotor contact surface are obtained by analytical method. Based on this, the torque model of the piezoelectric stator-drive motor is obtained. Then, the air-gap magnetic field model of the permanent magnet rotor is obtained by analytical method, and the electromagnetic stator-torque model is obtained. Finally, the torque model of the electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor is established by vector synthesis. The effects of piezoelectric stator mounting position angle, stator–rotor contact materials, and preload on motor torque are analyzed by simulation. The advantages of electromagnetic piezoelectric hybrid drive are analyzed, and the rationality of the model is preliminarily verified. It lays the foundation for further optimization design and performance improvement of electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

Dynamic Motion Analysis of Plane Mechanisms With Coulomb and Viscous Damping via the Joint Force Analysis

1975 ◽  
Vol 97 (2) ◽  
pp. 551-560 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Dynamic Equilibrium ◽  
Viscous Damping ◽  
Force Analysis ◽  
Initial Value ◽  
Damping Force ◽  
Joint Force ◽  
Coulomb Damping ◽  
Dynamic Motion ◽  
Joint Forces ◽  
Input Torque

Analysis of response of determinate plane mechanisms to known driving input force, or input torque, via the joint force analysis is presented. Coulomb damping and viscous damping forces in the pair bearings are included. Equations of dynamic equilibrium are solved for the components of the normal joint forces and for the motion of the mechanism as initial-value problems. The rotation of the resultant joint force, due to the fact that the pair member on a link is the inner member or the outer member of the pair, is considered by defining a generalized Coulomb damping force. Links of the mechanisms are considered rigid. The plane 4R and slider-crank switch mechanisms are investigated. Explicit solutions and numerical examples are given.

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