Numerical Formulations for Computing Design Propagations of the Spatial Slider-Crank Mechanism

1996 ◽  
Author(s):  
Hong-Liu Zou ◽  
Karim Abdel-Malek ◽  
Jia-Yi Wang
Keyword(s):  
Spanning Tree ◽  
Design Parameters ◽  
Coordinate Space ◽  
Joint Position ◽  
Link Length ◽  
Closed Loops ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Numerical Formulation ◽  
Crank Mechanism

Abstract A numerical formulation for studying the design of a spatial slider-crank mechanism is developed and illustrated. The mechanism is modeled using graph theory and closed loops are converted to a spanning tree structure by cutting joints and introducing new constraints. Variations of these constraints with respect to design parameters are derived. A change in link length or link orientation is propagated through the model and a new assembled configuration is computed hence redesigning the mechanism. Constraints are formulated in Cartesian space but computed in relative joint coordinate space. The Jacobian of the constraint is transformed to joint coordinate space in order to compute an assembled configuration for the cut-joint constraint formulation. The experimental code is illustrated through numerical examples where joint-position vectors and orientation matrices are altered.

Analytical Criteria for the Analysis of Design Propagations in Mechanisms

1996 ◽  
Author(s):  
Hong-Liu Zou ◽  
Karim Abdel-Malek ◽  
Jia-Yi Wang
Keyword(s):  
Graph Theory ◽  
Design Variable ◽  
Jacobian Matrix ◽  
Suspension System ◽  
Joint Position ◽  
Closed Loops ◽  
Numerical Example ◽  
Cartesian Space ◽  
Spatial Mechanisms ◽  
Joint Coordinates

Abstract A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

scholarly journals Design Propagation in Mechanical Systems: Kinematic Analysis

1997 ◽  
Vol 119 (3) ◽  
pp. 338-345 ◽  
Author(s):  
H. Zou ◽  
K. A. Abdel-Malek ◽  
J. Y. Wang
Keyword(s):  
Graph Theory ◽  
Design Variable ◽  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Mechanical Systems ◽  
Joint Position ◽  
Closed Loops ◽  
Cartesian Space ◽  
Spatial Mechanisms ◽  
Joint Coordinates

A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

Tolerance Analysis of a Robot Manipulator Having Uncertainties in Joint Clearance and Axis Orientation

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Se Jeong Lee ◽  
Jonathan A. Wickert ◽  
Hong Hee Yoo
Keyword(s):  
Robot Manipulator ◽  
Statistical Design ◽  
Tolerance Analysis ◽  
Joint Clearance ◽  
Design Parameters ◽  
Positional Error ◽  
Link Length ◽  
Axis Orientation ◽  
Manufacturing Tolerances ◽  
Clearance Model

The operating positional error of a robot manipulator, which develops inevitably because of manufacturing tolerances and assembly clearances, is preferentially maintained within a certain range in order to achieve an acceptable level of performance and accuracy. Because additional cost is incurred when manufacturing tolerances are tightened, an alternative design strategy maximizes the tolerances (so as to reduce the cost) while minimizing positioning error (to satisfy a performance requirement). In this paper, a new joint clearance model is developed for spatial mechanisms that incorporate revolute joints, which in turn are subjected to specified tolerance or uncertainty in the orientation of their axes. Statistical design parameters related to variations of link length and joint axis orientation are identified from the clearance model. The statistical influence of the design parameters on the robot manipulator’s response is investigated through a general multibody dynamics sensitivity formulation. The method offers substantial improvement in computational efficiency when compared to the Monte Carlo procedure. The uncertainty in orientation of a revolute joint’s axis influences the positioning accuracy of the robot manipulator’s response to a greater degree than does uncertainty in the length of a link.

scholarly journals LOOP EQUATION AND AREA LAW IN TURBULENCE

1994 ◽  
Vol 09 (08) ◽  
pp. 1197-1238 ◽  
Author(s):  
A. A. MIGDAL
Keyword(s):  
Fluid Dynamics ◽  
Summer School ◽  
Spatial Scales ◽  
Inertial Range ◽  
Coordinate Space ◽  
Extended Version ◽  
Closed Loops ◽  
Loop Equation ◽  
Minimal Area ◽  
Area Law

This is an extended version of the preprint,4 based on the lectures given at Cargese Summer School and Chernogolovka Summer School in 1993. The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. We derive explicit functional equation for the pdf of the circulation PC (Γ) which allows the scaling solutions in the inertial range of spatial scales. The pdf decays as exponential of some power of Γ3/A2, where A is the minimal area inside the loop.

Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

1999 ◽  
Author(s):  
Apiwat Reungwetwattana ◽  
Shigeki Toyama
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Analysis Method ◽  
Stabilization Method ◽  
Kinematic Constraint ◽  
Constraint Violation ◽  
Closed Loops ◽  
Constraint Stabilization ◽  
Constraint Equations ◽  
Crank Mechanism

Abstract This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.

A Study on Optimum Design Using Fuzzy Numbers As Design Variables

1995 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa
Keyword(s):  
Fuzzy Sets ◽  
Optimum Design ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Design Variables ◽  
Conventional Methods

Abstract In this study, we summerize the method of fuzzy optimization using fuzzy numbers as design variables. In order to detect flaw in fuzzy calculation, we use LR-fuzzy numbers, which is known as its simplicity in calculation. We also use simple fuzzy numbers’ operations, which was proposed in the previous papers. The proposed method has unique characteristics that we can obtain fuzzy sets in design variables (results of the design) directly from single numerical optimizing process. Which takes a large number of numerical optimizing processes when we try to obtain similar results in the conventional methods. In the numerical examples, we compare the proposed method with several other methods taking imprecision in design parameters into account, and demonstrate the effectiveness of the proposed method.

Effects of the design parameters on the synthesis of Geneva mechanisms

2012 ◽  
Vol 227 (9) ◽  
pp. 2000-2009 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea
Keyword(s):  
Shock Loading ◽  
General Algorithm ◽  
Design Parameters ◽  
Kinematic Synthesis ◽  
Numerical Examples

A general algorithm for the kinematic synthesis of Geneva mechanisms with curved slots is introduced here, when a suitable displacement program is given with the aim of avoiding the typical shock-loading problems of conventional Geneva mechanisms. Moreover, the effects of the design parameters are analyzed through significant numerical examples. These parameters are: number of driving cranks; number of slots; imposed displacement program; and pin radius of the driving crank for the Geneva mechanism.

Reconnexion of lines of force in rotating spheres and cylinders

1966 ◽  
Vol 291 (1424) ◽  
pp. 60-72 ◽  
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Magnetic Force ◽  
Analytic Solution ◽  
Transient Phase ◽  
General Behaviour ◽  
Closed Loops ◽  
Numerical Examples ◽  
Conducting Sphere ◽  
Approximate Expressions

A solid conducting sphere or cylinder begins to rotate suddenly from rest in an initially uniform magnetic field. An analytic solution for this problem is obtained and it is shown that lines of magnetic force reconnect to form closed loops during the transient phase. The general behaviour of the system is investigated for all conductivities. Numerical examples are given and approximate expressions derived in the limiting cases of large conductivity and time.

Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry

2011 ◽  
Vol 225 (4) ◽  
pp. 975-986 ◽  
Author(s):  
Y-C Chen ◽  
M-L Gu
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Contact Analysis ◽  
Design Parameters ◽  
Stress Distributions ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Numerical Examples ◽  
Bearing Contact ◽  
Parallel Axis

This article investigated the contact behaviours of a modified curvilinear gear set for parallel-axis transmission, which exhibits a pre-designed parabolic transmission error (TE) and localized bearing contact. The proposed gear set is composed of a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. Tooth contact analysis enabled the authors to explore the influences of assembly errors and design parameters on TEs and contact ellipses of this gear set. It is observed that TEs were continuous and the contact ellipses were localized in the middle of the tooth flanks, even under assembly errors. Finite-element contact analysis was performed to study stress distributions under different design parameters. In addition, numerical examples are presented to demonstrate the contact characteristics of the modified curvilinear gear set.

Design of Spatial Non-Anthropomorphic Articulated Systems Based on Arm Joint Constraint Kinematic Data for Human Interactive Robotics Applications

2015 ◽  
Author(s):  
Hyosang Moon ◽  
Nina P. Robson
Keyword(s):  
Degrees Of Freedom ◽  
Wrist Joint ◽  
Design Parameters ◽  
Human Hand ◽  
Link Length ◽  
Hand Motion ◽  
Motion Constraints ◽  
Hand Kinematics ◽  
Minimum Jerk ◽  
Articulated Systems

The design of human interactive robotic systems requires additional considerations compared to conventional robotic designs to take into account human factors. In this paper, a recently developed linkage kinematic synthesis incorporating higher order motion constraints is utilized to the synthesis of a five degree of freedom serial TS linkage for human interactive applications. The T represents a universal two degrees-of-freedom shoulder, while the S defines a spherical three degrees-of-freedom wrist joint. The desired hand kinematics and its time derivatives can be obtained by a motion capture system as well as from the hand-object/environment contact geometries at two task locations. In order to determine the design parameters (i.e., locations of the base/shoulder and moving/wrist pivots, as well as the link length connecting these joints), position, velocity and acceleration constraint equations of the TS linkage are solved in the vicinity of the initial and the final reaching locations. The entire robotic joint trajectories are formulated via minimum jerk theory to closely approximate human natural hand profile with an elbow joint constraint. In this manner, the TS linkage system can be designed to guarantee to reproduce the natural human hand kinematics with the minimum amount of information about the desired hand kinematic specifications. The applicability of the proposed technique was verified by designing a TS linkage system from a captured human data, and then comparing the generated end-effector trajectory with the human hand motion trajectory, which show promising results.

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