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Kinematics of Machinery

by Jntu HeroesJntu Heroes
Type: NoteInstitute: Jawaharlal nehru technological university anantapur college of engineering Offline Downloads: 87Views: 2786Uploaded: 11 months ago

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Lecture notes on Kinematics
CONTENTS 1 INTRODUCTION.....................................................................................................4 2 KINEMATICS OF A PARTICLE..............................................................................9 2.1 Velocity....................................................................................................................... 10 2.2 Acceleration ............................................................................................................... 11 2.2.1 Classification of motion ....................................................................................... 12 2.3 Orthogonal transformation ....................................................................................... 14 2.3.1 Orthogonal Transformation of Vector Quantities.................................................. 14 2.3.2 Velocity in matrix form using the orthogonal transformation................................ 16 2.3.3 Acceleration in matrix form using the orthogonal transformation ......................... 16 particle in Cylindrical coordinate system - r , ϕ , z .................................................... 17 2.4.1 The position vector .................................................................................................. 17 The velocity ......................................................................................................... 17 2.4.2 2.4.3 The acceleration................................................................................................... 18 2.4.4 Special cases............................................................................................................ 18 2.4 2.5 Particle trajectory...................................................................................................... 19 2.5.1 Rectilinear motion................................................................................................ 19 2.5.2 Curvilinear motion................................................................................................... 20 Harmonic motion ....................................................................................................... 20 2.6 2.6.1 Composition of harmonic motions in the same direction ...................................... 22 2.6.2 Composition of two perpendicular harmonic motions........................................... 23 2.7 3 Motion of a set of particles ........................................................................................ 23 SOLID BODY MOTION......................................................................................... 24 3.1 Translation motion of a solid body........................................................................... 24 3.1.1 Investigating kinematic quantities ........................................................................ 24 3.2 Rotation of a solid body around fixed axis................................................................ 25 3.2.1 Finding the velocity of an arbitrary point.............................................................. 26 3.2.2 Finding the acceleration of an arbitrary point B.................................................... 27 3.2.3 Solid body kinematics consequences (the geometrical dependency) ..................... 29 3.3 Universal planar motion............................................................................................ 31 3.3.1 The position............................................................................................................ 31 2 Dr. Ing. Zdenka Sant 10/2009
3.3.2 3.3.3 The velocity ......................................................................................................... 32 The pole of motion............................................................................................... 33 3.3.4 Finding the acceleration ........................................................................................... 35 The instantenous centre of acceleration – the pole of acceleration........................ 37 3.3.5 3.4 centre of the trajectory curvature ............................................................................. 38 3.5 Combined motion ...................................................................................................... 41 3.5.1 Kinematical quantities by means of combined motion.......................................... 42 3.5.2 The velocity ......................................................................................................... 42 3.5.3 The acceleration................................................................................................... 42 3.5.4 Coriolis acceleration ............................................................................................ 43 3.5.5 Finding the pole of motion by means of combined motion ................................... 44 3.6 Spherical motion of a Body ....................................................................................... 45 3.7 universal Space Motion Of a body ........................................................................... 47 4 SYSTEM OF BODIES........................................................................................... 48 4.1 Simultaneous rotations around concurrent axes ...................................................... 48 4.2 Simultaneous rotations around parallel axes............................................................ 49
1 INTRODUCTION Design and analysis are two vital tasks in engineering. Design process means the synthesis during the proposal phase the size, shape, material properties and arrangements of the parts are prescribed in order to fulfil the required task. Analysis is a technique or rather set of tools allowing critical evaluation of existing or proposed design in order to judge its suitability for the task. Thus synthesis is a goal that can be reached via analysis. Mechanical engineer deals with many different tasks that are in conjunction to diverse working processes referred to as a technological process. Technological processes involve transportation of material, generation and transformation of energy, transportation of information. All these processes require mechanical motion, which is carried out by machines. To be able to create appropriate design of machine and mechanism the investigation of relation between the geometry and motion of the parts of a machine/mechanism and the forces that cause the motion has to be carried out. Thus the mechanics as a science is involved in the design process. Mechanics represents the science that includes Statics, Dynamics, and Mechanics of Materials. Statics provides analysis of stationary systems while Dynamics deals with systems that change with time and as Euler suggested the investigation of motion of a rigid body may be separated into two parts, the geometrical part and the mechanical part. Within the geometrical part Kinematics the transference of the body from one position to the other is investigated without respect to the causes of the motion. The change is represented by analytical formulae. Thus Kinematics is a study of motion apart from the forces producing the motion that is described by position, displacement, rotation, speed, velocity, and acceleration. In Kinematics we assume that all bodies under the investigation are rigid bodies thus their deformation is negligible, and does not play important role, and the only change that is considered in this case is the change in the position. Terminology that we use has a precise meaning as all the words we use to express ourselves while communicating with each other. To make sure that we do understand the meaning we have a thesaurus/glossary available. It is useful to clarify certain terms especially in areas where the terminology is not very clear. Structure represents the combination of rigid bodies connected together by joints with intention to be rigid. Therefore the structure does not do work or transforms the motion. Structure can be moved from place to place but it does not have an internal mobility (no relative motion between its members). Machines & Mechanisms – their purpose is to utilize relative internal motion in transmitting power or transforming motion. Machine – device used to alter, transmit, and direct forces to accomplish a specific objective. Mechanism – the mechanical portion of a machine that has the function of transferring motion and forces from power source to an output. Mechanism transmits motion from drive or input link to the follower or the output link.

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