Mechanics Place in Science Mechanisms and Structures Number Synthesis Paradoxes and Isomers Transformations and Inversions Grashof s Law
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1 INTODUCTION TO MECHANISM SYNTHESIS Mechanics Place in Science Mechanisms and Structures Number Synthesis Paradoxes and Isomers Transformations and Inversions Grashof s Law ME312: Dynamics of Mechanisms 1
2 The Ultimate Goal is to Synthesize Machine Elements Manufacturing Materials Statics Strength of Martials Advanced Strength Machine Design Mechanics Kinetics Dynamics Thermo-Fluids Kinematics ADV. DYN. & KINEMATICS MECHANISM DESIGN/SYNTHESIS Controls ME312: Dynamics of Mechanisms 2
3 Historical Perspective of Kinematics BC Archimedes of Syracuse Archimede s Screw Claw of Archimedes Heat ay Equilibrium of Planes Description of lever 1 st Century AD Hero of Alexandria Named Components Wedge, Lever, Screw, Windlass, & Pulley Jacob Leupold First to ecognize Machine Components 9 Volume Series of Books Published 1817 James Watt & Oliver Evans Straight-Line Linkage for Steam Engine Coupler Link Motion in 4-Bar BC Mesopotamia Lever Inclined Plane Wedge 28 BC Marcus Vitruvius De Architecture Earliest Writing on the Subject Moving Heavy Objects 1588 amelli Arteficiose Machine Describes Each Machine of the Time Without recognition of similarity of components Euler Mechanica Sive Motus Scienta Analytice Exposita Analytical Treatment of Mechanisms Planar Motion ME312: Dynamics of Mechanisms 3
4 Historical Perspective of Kinematics Early 1800 s Gaspard Monge L Ecole Polytechnic in Paris Inventor of Descriptive Geometry Course in Elements of Machines 1834 Europe and Andre-Marie Ampere Australia L Ecole Polytechnic Essai sur la Philosophie de Science First to use term Cinématique 1875 Franz euleaux Theoretische Kinematik Mechanism Synthesis 1940 s Interest Builds In US Early 1811 Jean Nicolas Pierre Hachette L Ecole Polytechnic in Paris First Mechanisms Book 1841 obert Willis University of Cambridge, England Mechanism Synthesis 1876 Alexander Kennedy Theoretische Kinematik Translated to English ME312: Dynamics of Mechanisms 4
5 Historical Perspective of Kinematics Machine de Marly (1684) Bachannan Paddle Wheel (1813) Created to pump water to the Gardens in the Palace of Versailles Delivered water to aqueduct 533 ft above river Pumps driven by parallelograph linkages ME312: Dynamics of Mechanisms 5
6 Machines/Kinetics and Mechanisms/Kinematics Machines: A combination of resistant bodies so arranged that by their means the mechanical forces of the nature can be compelled to do work accompanied by certain determinate motions. MECHANISMS: An assemblage of resistant bodies, connected by movable joints, to form a closed kinematic chain with one link fixed and having the purpose of transforming motion. Structures: An assemblage of resistant bodies connected by joints (or not) that do no work, and do not transfer motion. It is intended to be rigid. ME312: Dynamics of Mechanisms 6
7 Synthesis of Several Mechanisms will be Considered Gears Linkages CAMs Belts, Pulleys, And Chains ME312: Dynamics of Mechanisms 7
8 Mechanisms are Synthesized to Produce Various Types of Motion PLANA MOTION: All motion contained to one geometric Plane or Parallel Planes. ectilinear Translation: All Points of the body move in parallel straight line paths. TANSLATION otation: Each point the body remains a constant distance from a fixed axis that is perpendicular to the plane of motion. otation and Translation: Combination of the above two. OTATION COMBINATION ME312: Dynamics of Mechanisms 8
9 Curvilinear Translation a Special Case of Translation Curvilinear Translation: The paths of the points are identical curves parallel to a fixed plane. ME312: Dynamics of Mechanisms 9
10 Non-Planar Motion Can Also Be Generated By Mechanisms Helical Motion: each point of the body has motion of rotation about a fixed axis and at the same time has translation parallel to the axis. Spherical Motion: each point of the body has motion about a fixed point while remaining at a constant distance from it. Spatial Motion: the body moves with rotations about three non-parallel axes and translates in three independent directions. ME312: Dynamics of Mechanisms 10
11 Cycle, Period, and Phase of Motion Cycle: When the parts of a mechanism have passed through all the possible positions they can assume after starting from some simultaneous set of relative positions and have returned to their original relative positions. Period: The time required for a cycle of motion. Phase: The simultaneous relative position of a mechanism at a given instant during a cycle. ME312: Dynamics of Mechanisms 11
12 A Link Is A igid Body Having Two or More Nodes Unary Binary Ternary Quaternary Pentagonal Nodes/Pairing Elements: Points at which links can be attached. The order of the link is determined by the attachments used. Joints/Kinematic Pairs: Allows relative motion between links. Joint Classes: a kinematic pair is of the j th class if it diminishes the relative motion of linked bodies by j Degrees of Freedom (DoF) ME312: Dynamics of Mechanisms 12
13 Kinematic Chains are Formed by Connecting Links with Pairs Open Kinematic Chain: A chain with one or more open loops. Closed Kinematic Chain: A chain that forms one or more closed loops. Simple-Closed Chain: Chain consisting of entirely binary links and is closed. Compound Closed Chain: Chain including other than binary links that is closed. B B ME312: Dynamics of Mechanisms 13 P
14 Joint Classification, Kinematic Pairs Type of contact between elements Line Point Surface Degrees of Freedom Allowed Type of Physical Closure Force Form Higher Pairs Lower Pairs Number of Links Joined (Order) ME312: Dynamics of Mechanisms 14
15 Joint Closure Classified as Lower Pairs and Higher Pairs Form Closed, otating FULL Pin Joint Form Closed, Translating FULL Slider Joint Force Closed, Link against a plane HALF Joint Form Closed, Pin in Slot HALF Joint ME312: Dynamics of Mechanisms 15
16 Degrees of Freedom or Mobility The number of inputs needed to provide in order to create a predictable output The number of independent coordinates required to define its position P B B ME312: Dynamics of Mechanisms 16
17 1 DOF, Class I Kinematic Pairs as Defined by euleaux evolute () Prismatic (P) Helical (H) Lower Pair Contact Plainer & 3D Joint 1 DOF - Lower Pair Contact Plainer & 3D Joint 1 DOF - s Lower Pair Contact Plainer & 3D Joint 1 DOF Input -, Output s Input - s, Output - ME312: Dynamics of Mechanisms 17
18 2 DOF, Class II Kinematic Pairs as Defined by euleaux Cam (C a ) Cylinder (C) Slotted Spherical (S l ) Higher Pair Contact P Plainer & 3D Joint 2 DOF -,s Lower Pair Contact P 3D Joint 2 DOF s, Lower Pair Contact 3D Joint 2 DOF -, ME312: Dynamics of Mechanisms 18
19 3 DOF, Class III Kinematic Pairs as Defined by euleaux Spherical (S) Spherical Slotted Cylinder (C) Plane Pair (P l ) Lower Pair Contact 3D Joint 3 DOF:,, Lower Pair Contact P 3D Joint 3 DOF:,, s Lower Pair Contact P 3D Joint 2 DOF -,, s ME312: Dynamics of Mechanisms 19
20 4 DOF, Class IV Kinematic Pairs as Defined by euleaux Spherical Grove (S g ) Cylindrical Plane Pair (C p ) Lower Pair Contact P 3D Joint 4 DOF:,,, s Lower Pair Contact PP 3D Joint 4 DOF:,, s, t ME312: Dynamics of Mechanisms 20
21 5 DOF, Class V Kinematic Pairs as Defined by euleaux Spherical Plane (S p ) Lower Pair Contact PP 3D Joint 4 DOF:,,, s, t ME312: Dynamics of Mechanisms 21
22 Planar Mechanisms Each link has 3 DoF when moving relative to a fixed link n link planar mechanism (one link is considered FIXED) has 3(n-1) degrees of freedom before joints are connected Connecting a revolute pair 1 DoF 2 constraints 2 DoF 1 constraint Mobility of Mechanism Constraints of all joints minus total DoF of unconnected links ME312: Dynamics of Mechanisms 22
23 Mobility Calculation L- number of links M- mobility of planar n-link mechanism j 1- number of 1 DoF pairs j 2 - number of 2 DoF pairs Kutzbach Criterion M = 3 (L-1) - 2 j 1 - j 2 Grübler Criterion M = 3 (L-1) - 2 j 1 ME312: Dynamics of Mechanisms 23
24 Mobility Criterion: Kutzbach or Gruebler M=1 Mechanism can be driven by a single input direction M=2 Two separate input motions are necessary to produce constrained motion for the mechanism Differential Mechanism M=0 Motion is impossible and the mechanism is a structure Exact Constraint M=-1 edundant constraint Pre-Load ME312: Dynamics of Mechanisms 24
25 Example: Calculate the Mobility Slipping ME312: Dynamics of Mechanisms 25
26 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 26
27 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 27
28 Order of a Joint is One Less than the Number of Links Joined First order pin Joint Second order pin Joint ME312: Dynamics of Mechanisms 28
29 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 29
30 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 30
31 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 31
32 Kutzback Criterion for Half Joints Particular attention should be paid to the contact between the wheel and the fixed link Slipping ME312: Dynamics of Mechanisms 32
33 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 33
34 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 34
35 Spatial Mechanism Mobility Kutzbach Criterion M 6 ( L 1) 5 j 4 j 3 j 2 j j Where j 3-3 Dof joints j 4-4 Dof joints j 5-5 Dof joints ME312: Dynamics of Mechanisms 35
36 Mobility Paradoxes Over-constrained Linkage with edundant Constraint E-quintet, Delta Triplet M=0 E-quintet M=1 ME312: Dynamics of Mechanisms 36
37 Mobility Paradoxes Over-constrained Linkage with edundant Constraint ME312: Dynamics of Mechanisms 37
38 Mobility Paradoxes Passive or Idle Degree of Freedom ME312: Dynamics of Mechanisms 38
39 Example: Calculate the Mobility ME312: Dynamics of Mechanisms 39
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