Synthesis of a Spatial RRSS Mechanism for Path Generation Using the Numerical Atlas Method

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Wenrui Liu ◽  
Jianwei Sun ◽  
Jinkui Chu
Keyword(s):  
Rotation Angle ◽  
Synthesis Method ◽  
Path Generation ◽  
Feature Parameters ◽  
Atlas Method ◽  
Path Synthesis ◽  
The Mathematical Model ◽  
The Relationship ◽  
Generation Problem ◽  
Actual Size

Abstract An open path synthesis method for a spatial revolute-revolute-spherical-spherical (RRSS) mechanism is presented in this paper. The mathematical model for the trajectory curve is established. The characteristics of an RRSS mechanism in a standard installation position are revealed: the projection points of the coupler curve on the Oxy plane rotate by the corresponding input angles around the z-axis, and the generated points lie on an ellipse. Based on this finding, a 17-dimensional path generation problem can be translated into two lower-dimensional matching recognition problems and one actual size and installation position calculation problem. The path generation can be achieved by three steps. First, a database of four dimensional rotation angle parameters is established. By comparing the similarities between the mechanism feature curve of the prescribed open curve and its corresponding mechanism feature ellipse (MFE), the angles of installation, the initial angle of the input link, and the elliptic feature parameters of the desired RRSS mechanism can be approximately determined. Then, a 13-dimensional dynamic self-adapting numerical atlas database is established, which contains six basic dimensional types (BDTs) and seven wavelet feature parameters, and the BDTs of the desired RRSS mechanism are obtained. Finally, based on the relationship between the MFE of the prescribed curve and the BDTs of the desired RRSS mechanism, the calculation models for the actual link lengths and installation positions of the desired RRSS mechanism were established. Three examples are presented in this paper.

scholarly journals Homotopy Directed Optimization to Design a Six-Bar Linkage for a Lower Limb With a Natural Ankle Trajectory

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Brandon Y. Tsuge ◽  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Lower Limb ◽  
Polynomial System ◽  
Optimization Technique ◽  
Synthesis Method ◽  
Optimization Techniques ◽  
Path Generation ◽  
Optimization Strategy ◽  
Direct Solution ◽  
New Formulation ◽  
Path Synthesis

This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

A New Method of Dimensional Synthesis for Planar 4-Bar Path Generation With Prescribed Timing

1998 ◽  
Author(s):  
Wu Xin ◽  
Chu Jinkui ◽  
Wu Chen ◽  
Cao Weiqing
Keyword(s):  
Rotation Angle ◽  
New Method ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Angle Function ◽  
Mathematical Equations ◽  
Harmonic Components ◽  
Set Up ◽  
Path Synthesis ◽  
First Time

Abstract Mathematical equations for 4-bar path generation on an arbitrarily arranged mechanism are set up by using complex number and Fourier series theory in this paper. The harmonic components of path generation on the coupler are carried out by systematic study. According to the conception of Coupler Rotation-Angle Operator (in short CRAO) about coupler’s rotation-angle function, a new method of determining the position for a coupler point, real dimensions and installing dimensions of the linkage is established for the first time. Based on this thinking, the concrete steps of dimension synthesis for path generation with prescribed timing are formed, and the method of path synthesis by using harmonic characteristic parameters is developed and further prefect is made.

On the Solution of Multi-Precision-Point Path Synthesis of Planar Four-Bar Mechanisms Based on Solution Region Methodology

2018 ◽  
Author(s):  
Jianyou Han ◽  
Wupeng Liu
Keyword(s):  
Infinite Number ◽  
Feasible Solution ◽  
Synthesis Method ◽  
Path Generation ◽  
Number Of Solutions ◽  
Region Method ◽  
Different Types ◽  
Design Requirements ◽  
Solution Region ◽  
Path Synthesis

In this paper, the solution region synthesis method for multi-precision-point path synthesis of planar four-bar mechanisms is presented. The solution region method is to represent an infinite number of mechanism solutions in a plane, in which the x-coordinate and the y-coordinate of the plane are both taken as the concerned parameters of the mechanisms. Then the feature curves of the mechanisms can be expressed in the plane. Firstly, the synthesis equations for the multi-precision-point path synthesis of planar four-bar mechanisms are established. Then according to the proposed defect judgment method, the defective solutions are eliminated, and an infinite number of solutions without defects are obtained. After considering and imposing design requirements, the linkages of different types and different curve types are represented in the solution region. Finally, Taking the path generation of eight points as the example, the methodology of establishing the solution region and the feasible solution region are presented, and the synthesis results are illustrated.

Temperature Influence on Performance of Oxidation Ponds

1991 ◽  
Vol 24 (5) ◽  
pp. 85-96 ◽  
Author(s):  
Qingliang Zhao ◽  
Zijie Zhang
Keyword(s):  
Mathematical Model ◽  
Temperature Influence ◽  
Field Scale ◽  
Experiment Data ◽  
Computer Technique ◽  
Oxidation Pond ◽  
Optimum Model ◽  
Oxidation Ponds ◽  
The Mathematical Model ◽  
The Relationship

By means of simulated tests of a laboratory–scale oxidation pond model, the relationship between BOD5 and temperature fluctuation was researched. Mathematical modelling for the pond's performance and K1determination were systematically described. The calculation of T–K1–CeCe/Ci) was complex but the problem was solved by utilizing computer technique in the paper, and the mathematical model which could best simulate experiment data was developed. On the basis of experiment results,the concept of plug–ratio–coefficient is also presented. Finally the optimum model recommended here was verified with the field–scale pond data.

Numerical Simulation on Velocity Profiles of Mill Bearing Lubrication

2010 ◽  
Vol 145 ◽  
pp. 282-286
Author(s):  
Qing Xue Huang ◽  
Jian Mei Wang ◽  
Yu Gui Li ◽  
Li Feng Ma ◽  
Chun Jiang Zhao
Keyword(s):  
Cross Section ◽  
Velocity Profiles ◽  
Flow State ◽  
Oil Film ◽  
Velocity Gradients ◽  
Oil Flow ◽  
The Mathematical Model ◽  
The Relationship ◽  
General Velocity ◽  
Oil Film Pressure

No 460 oil-film bearing oil as the dedicated lubricant is regarded as the incompressible Newtonian fluid. To comprehensively analyze the real oil flow state, the mathematical model on velocity profiles, together with its dimensionless equations, is established, and the calculating program is developed to simulate the 3D velocity profiles and velocity gradients at different oil flow layers. The relationship between velocity profiles and the oil film pressure is discussed, and the velocity tendency is consistent with the general velocity profile of wedge cross section. The conclusions are beneficial to the further study on lubricating performances of heavy contact components and to prolong their service lives.

scholarly journals The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles

2017 ◽  
Vol 14 (133) ◽  
pp. 20170261 ◽  
Author(s):  
Tom Shearer ◽  
Chavaunne T. Thorpe ◽  
Hazel R. C. Screen
Keyword(s):  
Flexor Tendon ◽  
Extensor Tendon ◽  
Mechanical Tension ◽  
Superficial Digital Flexor Tendon ◽  
Microstructural Model ◽  
And Function ◽  
Nonlinear Elastic ◽  
The Mathematical Model ◽  
The Relationship ◽  
Fitting Parameters

A nonlinear elastic microstructural model is used to investigate the relationship between structure and function in energy-storing and positional tendons. The model is used to fit mechanical tension test data from the equine common digital extensor tendon (CDET) and superficial digital flexor tendon (SDFT), which are used as archetypes of positional and energy-storing tendons, respectively. The fibril crimp and fascicle helix angles of the two tendon types are used as fitting parameters in the mathematical model to predict their values. The outer fibril crimp angles were predicted to be 15.1° ± 2.3° in the CDET and 15.8° ± 4.1° in the SDFT, and the average crimp angles were predicted to be 10.0° ± 1.5° in the CDET and 10.5° ± 2.7° in the SDFT. The crimp angles were not found to be statistically significantly different between the two tendon types ( p = 0.572). By contrast, the fascicle helix angles were predicted to be 7.9° ± 9.3° in the CDET and 29.1° ± 10.3° in the SDFT and were found to be statistically highly significantly different between the two tendon types ( p < 0.001). This supports previous qualitative observations that helical substructures are more likely to be found in energy-storing tendons than in positional tendons and suggests that the relative compliance of energy-storing tendons may be directly caused by these helical substructures.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

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