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Design and Optimization of a One-Degree-Of-Freedom Six

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Design and Optimization of a One-Degree-Of-Freedom Six DESIGN AND OPTIMIZATION OF A ONE-DEGREE-OF-FREEDOM SIX-BAR LINKAGE KLANN MECHANISM BACHELOR OF TECHNOLOGY In MECHANICAL ENGINEERING By Dr . N. MOHAN RAO, M .E, Ph.D. Associate professor and Head of Mechanical Engineering Department Of Mechanical Engineering Department Of Mechanical Engineering UNIVERSITY COLLEGE OF ENGNEERING JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY KAKINADA VIZIANAGARAM CAMPUS 2009-2013 CERTIFICATE This is to certify that the project entitled “DESIGN AND OPTIMIZATION OF A ONE-DEGREE-OF-FREEDOM SIX-BAR LINKAGE, KLANN MECHANISM” is a bona fide work of MADUGULA JAGADEESH (09VV1A0332), YALAMATI VASU CHAITANYA KUMAR (09VV1A0360), REDDIPALLI REVATHI (09VV1A0313), during the period 19th February 2013 to 15th April 2013 and is submitted in the partial fulfilment of the requirements for the award of the degree in BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING from the JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY KAKINADA, UNIVERSITY COLLEGE OF ENGNEERING VIZIANAGARAM. Dr.N.MOHAN RAO, M.E., Ph.D. Associate professor & Head of Mechanical Engineering J.N.T.U.K.UNIVERSITY COLLEGE OF ENGNEERING VIZIANAGARAM. ACKNOWLEDGMENT It is needed with a great sense of pleasure and immense sense of gratitude that we acknowledge the help of these individuals. We owe many thanks to many people who helped and supported us during the writing of this report. We would like to express our deep sense of gratitude and regards to Dr. N.MOHAN RAO, M.E, Ph.D & Head of Mechanical Department, who initiated in taking up this project work. We are grateful to his persisting encouragement and valuable guidance in completing our project work successfully. We are thankful to his everlasting patience and valuable suggestions throughout my project work. We express our sincere thanks to our respected Prof.P.UDAYA BHASKAR, Principal of JNTUK, College of Engineering. We are thankful to all faculty members for extending their kind cooperation and assistance. Finally, we are extremely thankful to our parents and friends for their constant help and moral support. Abstract The purpose of this thesis is to contribute to the area of mechanism design and optimization of a single degree of freedom leg mechanism. The leg mechanism is considered to be the very energy efficient especially when walking on rough terrains. This Klann mechanism requires very simple controls since a large actuator is required to drive the leg. First, a kinematic analysis is carried out on the mechanism to calculate the angles made by the each link when the crank subtends an angle with the horizontal. This analysis focuses the use of analytical kinematic equations on the mechanism. Second, the locus traced by the end point of the open loop mechanism is found out by using trignometrical relations. A C program is developed to find the angles made by the each link and the locus traced by the end point. Then a locus with a desired step length and step height is taken with an arbitrary link lengths. The above locus is called desired locus. Finally an optimization technique called genetic algorithm along with the above C program is used to find out the optimized link lengths of the mechanism. TABLE OF CONTENTS Chapter-1 INTRODUCTIION 1.1 Introduction 1.2 Literature Survey 1.3 Objectives of Present Work Chapter-2 KLANN LINKAGE 2.1 Introduction 2.2 Description 2.3 Design of Linkage 2.4 Analysis of walking motion 2.5 Advantages and disadvantages of Klann linkage over wheels or tracks 2.5.1 Advantages 2.5.2 Disadvantages 2.6 Applications of Klann Linkage Chapter-3 SYNTHESIS 3.1 Introduction to Synthesis 3.2 Type, Number and Dimension Synthesis 3.3 Graphical and Analytical Synthesis 3.3.1 Graphical Synthesis 3.3.2 Analytical Synthesis Chapter-4 SYNTHESIS OF KLANN LINKAGE 4.1 Position Analysis of Klann Linkage 4.2 C Program for Locus Co-ordinates Chapter-5 OPTIMIZATION 5.1 Introduction 5.2 Dimensional Synthesis of Klann Mechanism through Optimization 5.3 Genetic Algorithm 5.4 Formulation of Objective Function 5.5 Steps followed in calculating optimized link lengths for a certain Step Length and Height Chapter-6 CALCULATIONS AND RESULTS 6.1 Table of arbitrary link lengths and target co-ordinates 6.2 Output of Genetic Algorithm 6.3 Table comparing the target and generated co-ordinates Chapter-7 CONCLUSIONS Chapter-8 REFERENCES Chapter-1 1.1 Introduction: It has been established that off-road vehicles with legs exhibit better mobility, obtain higher energy efficiency and provide more comfortable movement than those of conventional tracked or wheeled vehicles while moving on rough terrain. So there is necessity to analyse & develop these leg mechanisms in order to meet various applications. Klann mechanism is one of these leg mechanisms which consists of six-links which is used as an alternative for wheels. Each wheel is replaced by two Klann mechanisms whose cranks are 180 degrees out of phase. To provide mobility for the mechanism required number of links and dimensional synthesis of links is required. This mechanism is used as a replacement of wheels finds applications in planetary exploration, walking chairs for the disabled and for military transport, rescue in radioactive zones for nuclear industries and in other hostile environments. 1.2 Literature Survey: In 1770, Richard Edgeworth tried to construct a wooden horse with 8 legs to jump over high walls however 40 years of experimentation was unsuccessful in constructing such a mechanism. In 1968, General Electric developed a walking truck that was capable of walking 5 mph and in 1976, Frank and McGhee made the first computer controlled walking machine. More recently, a Mechatronics Research Group from the University of Southern Queensland created a pneumatically powered quadruped and Applied Motion Inc, created a Spring Walker bipedal exoskeleton. Type synthesis has been one of the focuses for the early research on design of leg mechanisms, where slider-crank mechanisms and multiple cam mechanisms have been used. It was recommended to use only revolute joints for leg walking machines due to the difficulties in lubrication and sealing of the sliding joints, which is essential for the machines to walk outdoors. Many pin-joined legged mechanisms have been designed, which are often compound mechanisms consisting of a four-bar linkage and a pantograph. The potential advantages of such compound mechanisms are fast locomotion, minimal energy loss, simplicity in control design, and the slenderness of the leg. There have been many investigations on the adequate degrees-of-freedom (DOF) for each leg mechanism. Depending on the desired functional Page | 1 requirements (flexibility, speed, etc.) and walking environment, the legged walkers can have up to eight legs and a total of eighteen active DOF. Another example is the adaptive Suspension vehicle developed by Ohio State University, which has six legs and eighteen DOF. In general, it has been accepted that three DOF for each leg is required to provide high mobility, one for providing back-and-forth, one for up-and-down motion of the foot and one for turning. However, it has been discussed that unlike a ground-based manipulator that can be operated with an off-board power supply, a walking machine has to carry the entire power supply in addition to the external payload and the weight of the machine body. Thus, it is desirable to use a small number of actuators to reduce the body weight and to simplify the motion coordination. A number of six-link and seven-link leg mechanisms have been designed with one degree-of-freedom. Rigorous research has been carried out on their mobility and energy loss through kinematic and structural analysis. Two important findings have been documented: A crank as an input link with continuous rotation motion should be used to achieve fast motion with minimum control An ovoid foot path is necessary to step over small obstacles without raising the body too much height. These two requirements are important for designing single-DOF leg mechanisms for mobility and energy efficiency. 1.3 OBJECTIVES OF PRESENT WORK Many techniques for the synthesis of linkages are invented in recent years. Most of these approaches are involved techniques and are mathematically complicated. Only few of them allow a closed from solution. Of these, optimization procedures attempting to minimize an objective function play an important role. A set of inequality constraints that limit the range of variation of parameters may be included in the calculation. The new values of linkage parameters are generated with each iteration step according to particular optimization scheme used. The closest achievable fit between the calculated points and desired points is sought. Even the desired points will Page | 2 not exactly match but this is considered as acceptable result for most engineering tasks. Each optimization approach has as own advantages and disadvantages in term of convergence accuracy, reliability, complexity and speed. Some methods converge even to a minimum value of objective they may not be the best solution. Based on this points there is a lot of scope for application of new methods of optimization for six-bar synthesis problem. Following are the main objective of the present work: (1) Path synthesis of Klann mechanism. (2) Implementation of genetic algorithm optimization scheme. (3) Compare the obtained locus with the desired locus and finding offset to each precision point. Page | 3 Chapter-2 KLANN LINKAGE 2.1 Introduction: Linkages can be made to provide almost any movement required these movements can often be quite complex, but few linkages can match the complexity of those walking linkages created by nature-legs. Joseph Klann emulated the complex movement of linkages which is similar to the movement natural gait. The klann linkage is a open loop six-bar planar mechanism designed to simulate the gait of legged animal and function as a wheel replacement.
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