The Creation of the Mathematical Model of Involute Gear Modeling

2014 ◽  
Vol 912-914 ◽  
pp. 819-823
Author(s):  
Yan Hong Shi ◽  
Shuang Yao ◽  
Xin Yao
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Mechanical Design ◽  
Data File ◽  
Cnc Machining ◽  
Basic Knowledge ◽  
Involute Gear ◽  
Solid Edge ◽  
The Mathematical Model ◽  
Gear Accuracy

The paper puts forward a way to establish the mathematical model of involute gear according to the basic knowledge of mechanical design and method of mathematical analysis. A data file of coordinates of a series of points is generated by the use of powerful data analysis and mathematical calculation function of Excel. Based on this, involute and helix of high precision are designed through the seamless joint of Solid Edge and Excel. Then accurately modeling of involute gear can be realized. After modeling, high-precision gear can be manufactured through CNC machining to meet the equipment requirements for gear accuracy.

Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

An Optimization of Automated Process Planning for Manufacturing Prismatic Parts on a Machining Center

2015 ◽  
Vol 789-790 ◽  
pp. 1270-1274
Author(s):  
Janjira Kongchuenjai ◽  
Suksan Prombanpong
Keyword(s):  
Mathematical Model ◽  
Process Planning ◽  
Cutting Tools ◽  
Cnc Machining ◽  
Total Production ◽  
Machining Time ◽  
Optimal Sequence ◽  
Machining Center ◽  
Prismatic Parts ◽  
The Mathematical Model

One of the objectives of process planning optimization is to diminish machining time. Nowadays a lot of research papers presented different algorithms to solve this classic problem. Thus, the optimal sequence of parts in the machining operations by considering fixture faces, part faces, number of operations and number of tools is presented in this paper. The mathematical model based on the integer linear programming is developed to minimize the total production time of the prismatic parts manufactured on a CNC machining center equipped with the tombstone-type fixture. The time required for machining, tool traveling and tool changing is taken into consideration under relevant constraints such as precedence, fixture and available cutting tools. The optimal process plan can be obtained from the mathematical model and it is considered practical and acceptable.

scholarly journals MODELING OF HIGH PRECISION POSITIONING SYSTEM / DIDELIO TIKSLUMO PADĖTIES NUSTATYMO SISTEMOS MODELIAVIMAS

2013 ◽  
Vol 5 (6) ◽  
pp. 633-637
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Positioning System ◽  
Reduction Mechanism ◽  
Precision Positioning ◽  
Analytical Approaches ◽  
The Mathematical Model ◽  
Architecture Optimization ◽  
Fine Adjustment

This paper presents the modeling of a flexure-based precisionpositioning system for micro-positioning uses. The positioningsystem is featured with monolithic architecture, flexure-basedjoints and ultra fine adjustment screws. Its workspace has beenevaluated via analytical approaches. Reduction mechanism isoptimally designed. The mathematical model of the positioningsystem has been derived, which is verified by resorting to finiteelement analysis (FEA). The established analytical and (FEA)models are helpful for a reliable architecture optimization andperformance improvement of the positioning system. Santrauka Straipsnyje pristatomas didelio tikslumo centravimo ir niveliavimo padėties nustatymo sistemos su besideformuojančiais mechanizmais kūrimas ir modeliavimas. Padėties nustatymo sistema optimizuota Solidworks Simulation programiniu paketu. Centravimo platformų poslinkiams apskaičiuoti sudarytas matematinis modelis, kurio patikimumas buvo patikrintas taikant baigtinių elementų metodą. Sudaryto matematinio modelio ir rezultatų, gautų pritaikius baigtinių elementų metodą, skirtumai buvo mažesni nei 10 %. Pasiūlyta modeliavimo metodika gali būti taikoma kuriant padėties nustatymo sistemas su besideformuojančiais mechanizmais.

Design a New Worm-Type Mechanism of Mobile Robot Applicable in Colonoscopy

2015 ◽  
Vol 799-800 ◽  
pp. 1011-1015
Author(s):  
Jae Hyun Park ◽  
In Ho Kim ◽  
Woong Hee Cho ◽  
Jung Wan Park ◽  
Hyun Seok Yang
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Mechanical Design ◽  
Human Colon ◽  
Experimental Result ◽  
Linear Motion ◽  
Wide Diameter ◽  
The Mathematical Model ◽  
Varying Environment ◽  
Diameter Change

This paper presents a new mechanical design of mobile robot which can travel in the condition of continuous varying environment, such as colon of human body. Especially, the human colon environment contains an intense diameter change. The suggested mechanical design is capable to adapt in wide diameter changing system by generating two basic motions, rotational and linear motion, with a single actuator. Prototypes is fabricated, and tested result is presented in this paper. Also, experimental result is compared with the mathematical model of the mechanism to verify the feasibility of the proposed mechanism.

A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears

1991 ◽  
Vol 113 (2) ◽  
pp. 174-181 ◽  
Author(s):  
Z. H. Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Cnc Machining ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Finite Element Stress Analysis ◽  
Tool Setting ◽  
Spiral Bevel ◽  
The Mathematical Model ◽  
Made In

A complete tooth geometry of the circular-cut spiral bevel gears has been mathematically modeled. The mathematical model has been divided into several independent modules, each representing an individual kinematic relation or tool-setting, with examples included. A comparison with the spiraloid model has also been made in this paper. The mathematical model can be applied to simulate and calculate the tooth profiles for the Duplex Method, Helical Duplex Method, Formate Method, and Modified Roll Method for circular-cut spiral bevel gears. It can also be applied to the computer numerical controlled (CNC) machining, computer-aided finite element stress analysis, and tooth contact analysis (TCA) for the spiral bevel gear.

Programming of Automation and Trace Control for a Snake Form Robot

2011 ◽  
Vol 474-476 ◽  
pp. 1330-1333
Author(s):  
Pai Shan Pa ◽  
J.M. Shyu
Keyword(s):  
Mathematical Model ◽  
Inverse Kinematics ◽  
Model Transformation ◽  
Mechanical Design ◽  
Design Rule ◽  
Future Application ◽  
Motion System ◽  
Forward And Inverse Kinematics ◽  
The Mathematical Model ◽  
The Relationship

The motion system of a toy robotic snake is discussed. This study is expected to provide the best design for this toy and to help widen future application. A mathematical model was constructed after a literature and mechanical design survey. Tribotix AI 1001 motors are used to operate the snake. By an analysis of the mathematical model, transformation of the D-H matrices, and the introduction of forward and inverse kinematics, the relationship between the angle and the coordinate of each section of the robotic snake were determined. The trace curve of a real snake was also studied to arrive at a description of the motion and parameter changes for the robotic snake within a single time unit. MATLAB was used for the simulation and to plot the figures. Experiments and trace analyses were also performed to obtain the design rule and an approach to an improved mechanism for the toy robotic snake. Finally, the experimental results and the possibility of future development are discussed.

scholarly journals MODELING OF HIGH PRECISION POSITIONING SYSTEM / DIDELIO TIKSLUMO PADĖTIES NUSTATYMO SISTEMOS MODELIAVIMAS

2013 ◽  
Vol 5 (6) ◽  
pp. 638-641 ◽  
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Positioning System ◽  
Reduction Mechanism ◽  
Precision Positioning ◽  
Analytical Approaches ◽  
The Mathematical Model ◽  
Architecture Optimization ◽  
Fine Adjustment

This paper presents the modeling of a flexure-based precisionpositioning system for micro-positioning uses. The positioningsystem is featured with monolithic architecture, flexure-basedjoints and ultra fine adjustment screws. Its workspace has beenevaluated via analytical approaches. Reduction mechanism isoptimally designed. The mathematical model of the positioningsystem has been derived, which is verified by resorting to finiteelement analysis (FEA). The established analytical and (FEA)models are helpful for a reliable architecture optimization andperformance improvement of the positioning system. Santrauka Straipsnyje pristatomas didelio tikslumo centravimo ir niveliavimo padėties nustatymo sistemos su besideformuojančiais mechanizmais kūrimas ir modeliavimas. Padėties nustatymo sistema optimizuota Solidworks Simulation programiniu paketu. Centravimo platformų poslinkiams apskaičiuoti sudarytas matematinis modelis, kurio patikimumas buvo patikrintas taikant baigtinių elementų metodą. Sudaryto matematinio modelio ir rezultatų, gautų pritaikius baigtinių elementų metodą, skirtumai buvo mažesni nei 10 %. Pasiūlyta modeliavimo metodika gali būti taikoma kuriant padėties nustatymo sistemas su besideformuojančiais mechanizmais.

Compliant Five Bar Mechanism Control to Achieve a Desired Trajectory

2017 ◽  
Author(s):  
Ayse Tekes
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Path Tracking ◽  
Reference Trajectory ◽  
Compliant Joints ◽  
Torsional Spring ◽  
Short Beam ◽  
The Mathematical Model

In this study, two degrees of freedom planar compliant five-bar mechanism design is explored and synthesized to achieve a desired trajectory and to perform various defined tasks. The mechanism consists of five rigid links (including the ground) connected by the compliant large deflecting short beam joints and it is excited by the applied torques at the base links. The compliant five bar mechanism has not been explored in the literature for either a path tracking task or a function generation problem. The novelty of the compliant five bar mechanism presented in this paper is its large deflecting/rotating pivots joining the mechanism links. The mathematical model of the compliant five-bar mechanism is derived by using vector loop closures and dynamic inertia equations of the mechanism links. The dynamic response of the mechanism is investigated under the applied torques to the corresponding base links, using numerical 4th order Runge-Kutta methods. Compliant joints are represented by their equivalent torsional spring parameters so that the nonlinear large deflection equations of short beam joints are eliminated from the kinematic equations of the system using its equivalent Pseudo Rigid Body Model (PRBM). The torsional spring constants can be obtained, either by using nonlinear exact mathematical equations or by using geometrically nonlinear Finite Element Method software. The scope of this research is to derive a mathematical model of the system and to analyze the compliant five bar mechanism including the controller design for arbitrary predefined tasks to achieve the desired path for the end effector. The compliant five-bar mechanisms are superior to traditional rigid five-bar mechanisms in high precision tasks since compliant joints and links have no backlash and friction. This study explores path generation of compliant five bar mechanism resulting in high precision path tracking. The presented mechanism might be manufactured as a single piece using an injection molding technique or 3D printing by polypropylene and it is also suitable for a fully compliant Micro Electro Mechanical System fabrication. The mathematical model of the mechanism is validated by utilizing inverse-forward dynamic model. The tip point of the mechanism successfully follows the reference trajectory by employing model based PID controller.

scholarly journals Chimney Sweeping Robot Based on a Pneumatic Actuator

2021 ◽  
Vol 11 (11) ◽  
pp. 4872
Author(s):  
Peter Ján Sinčák ◽  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada ◽  
Zdenko Bobovský ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Mechanical Design ◽  
Pneumatic Actuator ◽  
Robot Motion ◽  
Experimental Measurements ◽  
Sweeping Process ◽  
Real Robot ◽  
The Mathematical Model

The need of improving the quality of professions led to the idea of simplification of processes during chimney sweeping. These processes have been essentially the same for tens of years. The goal of this paper is to bring an automation element into the chimney sweeping process, making the job easier for the chimney sweeper. In this paper, an essentially in-pipe robot is presented, which uses brushes to move while simultaneously cleaning the chimney or pipeline. The problem of the robot motion was reduced using an in-pipe robot due to the environments and obstacles that the robot has to face. An approach of using a pneumatic actuator for motion is presented along with the mechanical design. The next part of this paper is focused on the mathematical model of the robot motion, as well as its simulation and testing in the experimental pipeline. The simulations were compared with the experimental measurements and a few analyses were conducted describing the simulation model and its differences with the real robot, as well as considering certain parameters and their impact on the performance of the robot. The results are discussed at the end of the paper.

scholarly journals The Deformaton of The Gear Hob’s Generating Surfaces Due to Re-Sharpening

2018 ◽  
Vol 8 (1) ◽  
pp. 75-84
Author(s):  
Márton Máté ◽  
Dénes Hollanda
Keyword(s):  
Mathematical Model ◽  
Rake Face ◽  
Involute Gear ◽  
The Mathematical Model

Abstract The side relief faces of the monolithic involute gear hob are machined through relieving. The resulting surfaces are bevel helical surfaces in which the side cutting edges result from the intersection of these with the helical rake face. Theoretically, the gear hob is derived from an involute worm. Resharpening decreases the diameter of the hob, thus the edges became closer to the axis, and as a consequence they will be situated on a smaller worm than the original. The present paper analyses the deviation of the re-sharpened gear hob’s carrying worm from the theoretically perfect involute worm whose characteristic dimensions were adjusted considering the re-sharpened gear hob characteristic diameters. It was proven that the evolution of the errors is significantly different from that described in the literature. Thus, increasing the new gear hob diameters in comparison with the calculated dimensions is unnecessary, because it cannot reduce the error to half with this procedure. The mathematical model was built up accepting that the edges result from the intersection of an involute worm with a helical rake face and the side relief faces result from the rototranslation of the edges on a bevel helix leading curve dressed by the relieving parameter.

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