Overview. What is mechanism? What will I learn today? ME 311: Dynamics of Machines and Mechanisms Lecture 2: Synthesis

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1 Overview ME 311: Dynamics of Machines and Mechanisms Lecture 2: Synthesis By Suril Shah Some fundamentals Synthesis Function, path and motion generation Limiting condition Dimensional synthesis 1 2 What will I learn today? What is mechanism? 3 4 What is mechanism? Transformation of the motion 5 6 1

Define mechanism A mechanism is a device that transforms

any system can be defined using the number of degrees of

Definition The number of independent parametersneeded to

instant of time The number of inputswhich need to be provided

Rigid body motions Pure rotation One point on the body has no

Links A linkis a rigid body which possesses at least two

Pure translation All points on the body describe parallel

Complex motion A joint(also called kinematic pairs)is a

2 Define mechanism A mechanism is a device that transforms motion to some desirable pattern and typically develop little forces and transmit little power. What do we call a mechanism that develop significant force and transmit significant power? Machine 7 8 Mobility or Degrees Of Freedom ( DOF) Mobility of any system can be defined using the number of degrees of freedom (DOF). Definition The number of independent parametersneeded to uniquely define its position and orientationin space at any instant of time The number of inputswhich need to be provided in order to create a predictable output Position and orientation is w.r.t. frame of reference Rigid body assumption 9 10 Rigid body motions Pure rotation One point on the body has no motion with respect to the "stationary" frame of reference. Links A linkis a rigid body which possesses at least two nodesfor attachment to other links. Pure translation All points on the body describe parallel (rectilinear or curvilinear) paths. Complex motion A joint(also called kinematic pairs)is a connection between two or more links which allows some motion between the connected links. The body will change both its linear position and its angular orientation Points on the body will travel nonparallel paths At every instant, a center of rotation, which will continuously change location

3 Degrees of Freedom of Planar and Spatial Mechanisms Mobility of a planar mechanism can be given by M = 3(L-1) -2J 1 -J 2 Mobility of a spatial mechanism is be given by M = 6(L-1) -5J 1-4J 2-3J 3-2J 4 J 5 Each unconnected link in three-space has 6 DOF A one-freedom joint removes 5 DOF, a two-freedom joint removes 4 DOF, etc. Design of mechanisms Two fold objectives Synthesis of mechanisms in order to accomplish desired motions or tasks Analysisof mechanisms in order to determine their rigid-body dynamic behavior Number Synthesis Determination of the number and order of links and joints necessary to produce motion of a particular DOF 4-link, 6-link, 8-link, etc. Type Synthesis Refers to the definition of the proper type of mechanism best suited to the problem, e.g., Fourbar linkage, Slider crank, Cam-follower, etc Dimensional Synthesis Determination of the proportions (lengths) of the links necessary to accomplish the desired motions Path Generation Motion Generation Function Generation PATH GENERATION The control of a pointin the plane such that it follows some prescribed path. MOTION GENERATION The control of a linein the plane such that it assumes some prescribed set of sequential positions. FUNCTION GENERATION The correlation of an input motion with an output motion in a mechanism

Limiting Conditions Once a potential solution is found, it must be evaluated for its quality. Toggle position The toggle positions are determined by the colinearity of two of the moving links.

4 Limiting Conditions Once a potential solution is found, it must be evaluated for its quality. Toggle position The toggle positions are determined by the colinearity of two of the moving links. Some simple and quick evaluations. Toggle position Stationary positions Transmission angle Stationary positions Application Transmission angle Two-Position Dimensional Synthesis The angle between the output link and the coupler Rocker output (pure rotation) Coupler output (complex motion)

fourbarlinkage to move the link CD shown from position C 1 D 1 to C 2 D 2 (with moving pivots at C and D).

5 Design a fourbargrashofcrank-rocker to give θ of rocker rotation with equal time forward and back, from a constant speed motor input Design a fourbargrashofto move link CD from position C 1 D 1 to C 2 D Design a fourbarlinkage to move the link CD shown from position C 1 D 1 to C 2 D 2 (with moving pivots at C and D). Design a dyad to control and limit the extremes of the motion of the previous example to its two design position

6 Three-Position Dimensional Synthesis Dr. Suril V. Shah, IIIT-Hyderabad 31 Dr. Suril V. Shah, IIIT-Hyderabad 32 Solution Cognates Good solution that satisfies path generation constraints but inappropriate fixed pivots Cognate can be helpful in such situations. Cognate: Alinkage, of different geometry, which generates the same coupler curve. Roberts-Chebyschev Theorem: Three different planar, pin-jointed fourbarlinkages will trace identical coupler curves. Dr. Suril V. Shah, IIIT-Hyderabad 33 Dr. Suril V. Shah, IIIT-Hyderabad 34 Roberts Diagram Coupler point on link-3 Dr. Suril V. Shah, IIIT-Hyderabad 35 Dr. Suril V. Shah, IIIT-Hyderabad 36 6

7 THANK YOU 37 7

MENG 372 Chapter 3 Graphical Linkage Synthesis. All figures taken from Design of Machinery, 3 rd ed. Robert Norton 2003

MENG 372 Chapter 3 Graphical Linkage Synthesis All figures taken from Design of Machinery, 3 rd ed. Robert Norton 2003 1 Introduction Synthesis: to design or create a mechanism to give a certain motion