scholarly journals A Novel Analytical Solution Method for Constraint Forces of the Kinematic Pair and Its Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Changjian Zhi ◽  
Sanmin Wang ◽  
Yuantao Sun ◽  
Bo Li
Keyword(s):  
Solution Method ◽  
Solution Procedure ◽  
Dynamics Analysis ◽  
Kinematic Pair ◽  
Constraint Forces ◽  
Constraint Force ◽  
Spatial Mechanism ◽  
Observation Method ◽  
Crank Mechanism ◽  
Mechanism Theory

Constraint forces of the kinematic pair are the basis of the kinematics and dynamics analysis of mechanisms. Exploring the solution method for constraint forces is a hot issue in the mechanism theory fields. Based on the observation method and the theory of reciprocal screw system, the solution method of reciprocal screw system is improved and its solution procedures become easier. This method is also applied to the solution procedure of the constraint force. The specific expressions of the constraint force are represented by the reciprocal screw system of twist. The transformation formula of twist under different coordinates is given and it make the expression of the twist of kinematic pair more facility. A slider-crank mechanism and a single loop spatial RUSR mechanism are taken as examples. It confirms that this method can be used to solve the constraint force of the planar and spatial mechanism.

On the shaft locations of two contra-rotating counterweights for balancing spatial mechanisms

1997 ◽  
Vol 211 (8) ◽  
pp. 567-578 ◽  
Author(s):  
S-T Chiou ◽  
J-C Tzou
Keyword(s):  
Root Mean Square ◽  
Mean Square ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Crank Mechanism ◽  
Frequency Term ◽  
Shaking Moment

It has been shown in a previous work that a frequency term of the shaking force of spatial mechanisms, whose hodograph is proved to be an ellipse, can be eliminated by a pair of contrarotating counterweights. In this work, it is found that the relevant frequency term of the shaking moment is minimized if the balancing shafts are coaxial at the centre of a family of ellipsoids, called isomomental ellipsoids, with respect to (w.r.t.) any point on an ellipsoid, as is also the root mean square (r.m.s.) of the relevant frequency term of the shaking moment. It can also be minimized even though the location of either shaft, but not both, is chosen arbitrarily on a plane. The location of the second shaft is then determinate. In order to locate the centre, a derivation for the theory of isomomental ellipsoids of a frequency term of the shaking moment of spatial mechanisms is given. It is shown that the r.m.s. of a frequency term shaking moment of a spatial mechanism w.r.t. the concentric centre of the isomomental ellipsoids is the minimum. Examples of a seven-link 7-R spatial linkage and a spatial slider-crank mechanism are included.

Computational contact mechanics analysis of laterally graded orthotropic half-planes

2017 ◽  
Vol 14 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Onur Arslan
Keyword(s):  
Contact Mechanics ◽  
Solution Method ◽  
Solution Procedure ◽  
Engineering Applications ◽  
Linear Solution ◽  
Content Type ◽  
Analytical Technique ◽  
Computational Contact Mechanics ◽  
Mechanics Analysis ◽  
Contact Response

Purpose Frictional sliding contact problems between laterally graded orthotropic half-planes and a flat rigid stamp are investigated. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Design/methodology/approach The solution procedure is based on a finite element (FE) approach which is conducted with an efficient FE analysis software ANSYS. The spatial gradations of the orthotropic stiffness constants through the horizontal axis are enabled utilizing the homogeneous FE approach. The Augmented Lagrangian contact algorithm is used as an iterative non-linear solution method in the contact analysis. Findings The accuracy of the proposed FE solution method is approved by using the comparisons of the results with those computed using an analytical technique. The prominent results indicate that the surface contact stresses can be mitigated upon increasing the degree of orthotropy and positive lateral gradations. Originality/value One can infer from the literature survey that, the contact mechanics analysis of orthotropic laterally graded materials has not been investigated so far. In this study, an FE method-based computational solution procedure for the aforementioned problem is addressed. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Additionally, this study provides some useful points related to computational contact mechanics analysis of orthotropic structures.

With the Backlash Dynamics Simulation of a Crank-Slider Mechanism of the Internal Combustion Engine

2012 ◽  
Vol 215-216 ◽  
pp. 1081-1084
Author(s):  
Shao Jun Bo ◽  
Kui Ji ◽  
Juan Tian
Keyword(s):  
System Dynamics ◽  
Combustion Engine ◽  
Dynamics Simulation ◽  
Kinematic Pair ◽  
Body System ◽  
Nonlinear Characteristics ◽  
Preliminary Study ◽  
Multi Body ◽  
Dynamics Models ◽  
Crank Mechanism

On the basis of flexible multi-body system dynamics theory, we built flexible multi-body system dynamics models which include a backlash, and to a slider-crank mechanism as the research object, we made a preliminary study on the effect on the flexible components and the backlash of the kinematic pair on mechanical system dynamics characteristics. To consider the backlash of the kinematic pair and component of flexible space can show a preliminary research on the dynamic simulation, and focus on the backlash, friction and gravity field to influence in the dynamic characteristics of the system. The simulation results show that, due to the existence of backlash made the two components frequent collision in the process of the stretching, clearance, flexible and friction are closed, make the system nonlinear characteristics increased.

Dynamical Equations With Non-Ideal Constraints: New and Old Alternatives

2007 ◽  
Author(s):  
Arun K. Banerjee ◽  
Mark Lemak
Keyword(s):  
Equations Of Motion ◽  
Alternative Form ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Constraint Force ◽  
Kane’S Method ◽  
Kane's Method ◽  
Ellipsoidal Surface ◽  
Ideal Constraint ◽  
The Ideal

This paper deals with the motion of mechanical systems with non-ideal constraints, defined as constraints where the forces associated with the constraint do work. The first objective of the paper is to show that two newly published formulations of equations of motion of systems with such non-ideal constraints are unnecessarily complex for situations where the non-ideal constraint force does not depend on the ideal constraint force, because they introduce and then eliminate these non-working constraint forces. We point out that a method already exists for nonideal constraints, namely, Kane’s equations, which are simpler because, among other things, they are based on automatic elimination of non-working constraints. The examples considered in these recent publications are worked out with Kane’s method to show the applicability and simplicity of Kane’s method for non-ideal constraints. A second objective of the paper is to present an alternative form of equations for systems where the non-ideal constraint force depends on the ideal constraint force, as in the case of Coulomb friction. The formulation is shown to lend itself naturally to also analyzing impact dynamics. The method is applied to the dynamics of a slug moving against friction on a moving ellipsoidal surface. Such a crude model may simulate, in essence, propellant motion in a tank in zero-g, or during docking of a spacecraft.

Kinematic Modeling of the Variable Vector Propeller in Type of Disk Connecting-Rods

2011 ◽  
Vol 486 ◽  
pp. 57-60
Author(s):  
Feng Lai Li ◽  
Xin Chang ◽  
Fan Kai Kong ◽  
Zhi Bo Zhao
Keyword(s):  
Pitch Angle ◽  
Structural Parameters ◽  
Mechanism Analysis ◽  
Basic Design ◽  
Connecting Rod ◽  
Kinematic Modeling ◽  
Compact Structure ◽  
Spatial Mechanism ◽  
Blade Pitch Angle ◽  
Mechanism Theory

Variable vector propeller has characteristics of small compact structure and lightweight, and the thrust in any direction can be generated due to the cyclical change of blade pitch angle. The structure of a propeller is a complex spatial mechanism, so its kinematic analysis is the basis of controlling the propeller, the dynamics research, the structural parameters design and checking of the propeller. The propeller considering the mechanism of disk connecting rod variable pitch as the basic design is researched in this study. The mechanism analysis was carried out by means of the mechanism theory, the spatial kinematic modeling for bodies was completed, the motion relationship was derived and the related kinematic equations were obtained.

Constraint Forces and the Method of Auxiliary Generalized Speeds

2003 ◽  
Vol 70 (4) ◽  
pp. 568-574 ◽  
Author(s):  
S. Djerassi ◽  
H. Bamberger
Keyword(s):  
Multibody Systems ◽  
Computational Cost ◽  
Matrix Inversion ◽  
Constraint Forces ◽  
Constraint Force ◽  
Motion Equations ◽  
Reaction Forces

This paper deals with noncontributing forces, usually called constraint forces or reaction forces, arising in simple, nonholonomic multibody systems. These forces are related to two kinds of constraints, namely, kinematical constraints—derived from kinematical requirements, and auxiliary constraints, introduced for the purpose of constraint forces determination. Here, the method of “auxiliary generalized speeds” is used to bring into evidence constraint forces related to the two kinds of constraints. It is shown that auxiliary generalized speeds can always be chosen in a way that gives rise to additional equations each having one measure number of a constraint force as an unknown. Motion equations can thus be generated and solved without regard to constraint forces determination; and constraint forces can be determined with no matrix inversion, at a minimal computational cost.

scholarly journals КІНЕТОСТАТИЧНЕ ДОСЛІДЖЕННЯ ШАРНІРНИХ ПРОСТОРОВИХ МЕХАНІЗМІВ ГАЛТУВАЛЬНИХ МАШИН (ЧАСТИНА 2: ДОСЛІДЖЕННЯ МЕХАНІЗМУ МАШИНИ З ДВОМА РОБОЧИМИ ЄМКОСТЯМИ, ЩО З’ЄДНАНІ ПОСТУПАЛЬНОЮ КІНЕМАТИЧНОЮ ПАРОЮ)

2021 ◽  
pp. 20-28
Author(s):  
MARK ZALIUBOVSKYI ◽  
VLADYSLAVA SKIDAN
Keyword(s):  
Computer Aided Design ◽  
Practical Significance ◽  
Design System ◽  
Axial Distance ◽  
Kinematic Pair ◽  
Term Operation ◽  
Spatial Mechanism ◽  
Computer Aided ◽  
Allowable Range ◽  
Aided Design

Goal. Kinetostatic study of a statically defined hinged spatial mechanism without excessive (passive) connection of the shredding machine with two working tanks connected by a translational kinematic pair. Method. Radial and axial components of reactions in all rotating and translational kinematic pairs of the hinged statically defined spatial mechanism of the machine for processing of details with two working capacities connected among themselves by translational kinematic pair at its work at idling were determined on the basis of kinetostatic research. The study was performed using the computer-aided design system SolidWorks-2016 computer-aided design system, which performed a 3D model of a shredding machine with two working tanks connected by a translational kinematic pair. Results. 3D modeling of a shredding machine with two working tanks connected by translational kinematic pair in the computer-aided design system SolidWorks-2016 computer-aided design system is performed, maximum values of radial and axial components of reactions in all rotating and translational kinematic pairs of machine are determined, and the influence of total two working tanks for the increase of the maximum values of reactions in the kinematic pairs of the spatial mechanism of the machine. Scientific novelty. For the first time, the relationship between the total wheelbase of two working tanks and the change in the maximum values of reactions (axial and radial) in all rotating and translational kinematic pairs of the shredding machine was established. The allowable range of variation of the total wheelbase of two working tanks is determined, which creates conditions for long-term operation of the machine. Practical significance. It is established that the change of maximum values of radial and axial components of reactions in all rotating and translational kinematic pairs of the spatial mechanism of the galvanizing machine depends on the total axial distance of two working capacities of the machine. The obtained research results can be useful in the design of shredding equipment with complex spatial movement of working tanks.

Numerical Investigation of a Centrifugal Compressor for Supercritical CO2 Cycles

2020 ◽  
Author(s):  
Renan Emre Karaefe ◽  
Pascal Post ◽  
Marwick Sembritzky ◽  
Andreas Schramm ◽  
Francesca di Mare ◽  
...  
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Flow Field ◽  
Numerical Simulations ◽  
Centrifugal Compressor ◽  
Supercritical Co2 ◽  
Solution Method ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Test Loop

Abstract In this work, the performance characteristics and the flow field of a centrifugal compressor operating with supercritical CO2 are investigated by means of three-dimensional CFD. The considered geometry is based on main dimensions of the centrifugal compressor installed in the supercritical CO2 compression test-loop operated by Sandia National Laboratories. All numerical simulations are performed with a recently developed in-house hybrid CPU/GPU compressible CFD solver. Thermodynamic properties are computed through an efficient and accurate tabulation technique, the Spline-Based Table Look-Up Method (SBTL), particularly optimised for the applied density-based solution procedure. Numerical results are compared with available experimental data and accuracy as well as potentials in computational speedup of the solution method in combination with the SBTL are evaluated in the context of supercritical CO2 turbomachinery.

The Closed-Form Equation of Motion of a Human Body With Joint Friction

2013 ◽  
Author(s):  
Qingmin Huang ◽  
Ye-Hwa Chen ◽  
Xin Nie
Keyword(s):  
Closed Form ◽  
Human Body ◽  
Free Fall ◽  
Analytic Form ◽  
Equation Of Motion ◽  
Friction Torque ◽  
Constraint Forces ◽  
Constraint Force ◽  
Joint Friction ◽  
And Control

A general method for equation of motion of a human body is presented. The equation is in closed-form (i.e., analytic form). A hierarchical approach is introduced to get the equation of motion of the human body. The constraint force between subsystems is explicitly obtained which can be used to calculate the joint friction torque. The final equation of motion includes the dynamics of the unconstrained motion, the constraints, and the constraint forces including the joint friction torque induced by the nonideal constraints. No auxiliary variables such as Lagrange multipliers or pseudo-generalized speeds are needed. Therefore the equation of motion is most suitable for generic dynamic analysis and control design. A four-segment, planar, articulated linkage free fall human body is chosen to demonstrate this method.

A Vector Bond Graph Method of Kineto-Static Analysis for Complex Planar Linkage

2012 ◽  
Vol 482-484 ◽  
pp. 1062-1067
Author(s):  
Zhong Shuang Wang ◽  
Jian Guo Cao ◽  
Ji Chen
Keyword(s):  
Static Analysis ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Constraint Force ◽  
Graph Method ◽  
Algebraic Problem ◽  
Complete Form ◽  
Junction Structure ◽  
Force Vectors

For the kineto-static analysis of complex planar linkage, the procedure based on vector bond graph is proposed. The constraint force vectors at joints can be considered as unknown effort source vectors and added to the corresponding 0-junctions of the system vector bond graph model, most of the differential causalities in system vector bond graph model can be eliminated . In the case of mixed causality, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form. As a result, the very difficult algebraic problem caused by differential causality and nonlinear junction structure can be overcome, and the automatic kineto-static analysis of complex planar linkage on a computer is realized. By a practical example, the validity of this procedure is illustrated.

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