Theory of machines fundamentals
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Theory of machines fundamentals

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Theory of machines fundamentals Theory of machines fundamentals Presentation Transcript

  • Kinematics Fundamentals Chapter 2
  • Definitions • Mechanisms – A device which transform motion to some desirable pattern and typically develop very low forces and transmits little power • Machine – Typically contains mechanism which are design to provide significant forces and transmit significant power
  • http://www.flyingmachines.org/davi.html www.gizmag.com/pictures/hero/3533_01.jpg
  • http://4dlab.info/images/engine_cutaway.jpg www.50classicchevy.com/images/1950-chevrolet
  • Kinematics Fundamentals • Degree of Freedom (DOF) – The system’s DOF equal to the number of independent parameters(measurement) which are needed to uniquely define its position in space at any time
  • Kinematics Fundamentals • Types of Motion –Pure translation –Pure rotation –Complex motion
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – A link is an rigid body which possesses at least two nodes which are points for attachment to other links
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – A joints (kinematic pairs) is a connection between two or more links, which allows some motion, or potential motion, between the connected links – Classification • Type of contact between the elements, line, point, or surface • Number of DOF allowed at the joint
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Classification • Type of physical closure of the joint • Number of links joined – Type of Contact • Lower pair (full joints) – Describe joints with surface contact
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Type of Contact • Lower pair
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Type of Contact • Higher pair – Describe joints with point or line contact
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Number of DOF allowed Joint • One DOF (full joint)
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Number of DOF allowed Joint • Two DOF (half joint/roll-slide)
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Type of Physical Closure • Form closed- closed by its geometry • Force closed- closed by an external force
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Number of links joined • Order of the joint: the number of links minus one
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Kinematic Chain • An assemblage of links and joints, interconnected in a way to provide a controlled output motion in response to a supplied input motion – Mechanism • A kinematic chain in which at least one link has been “grounded,” or attached, to the frame of reference
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Machine • A combination of resistant bodies arranged to compel the mechanical forces of nature to do work accompanied by determinate motions
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Ground • Any link or links that are fixed with respect to the reference frame – Crank • A link which makes a complete revolution and is pivoted to ground
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Rocker • A link which has oscillatory (back and forth) rotation and pivoted to ground
  • Kinematics Fundamentals • Links, Joints, and Kinematic Chains – Coupler • A link which has complex motion and is pivoted to ground
  • Kinematics Fundamentals • Determining DOF – DOF or Mobility • The number of inputs which need to be provided in order to create a predictable output • The number of independent coordinates required to define its position – Open or Closed – Dyads
  • Kinematics Fundamentals • Determining DOF – DOF in Planar Mechanisms • Gruebler’s Equation where – M = degree of freedom or mobility – L = number of links – J = number of joints – G = number of grounded links GJLM 323 
  • Kinematics Fundamentals • Determining DOF – DOF in Planar Mechanisms • Gruebler’s Equation • If more than one link is grounded, the net effect will be to create one larger, higher- order ground link. G is always one, therefore GJLM 323    JLM 213 
  • Kinematics Fundamentals • Determining DOF – DOF in Planar Mechanisms • Kutzbach Equation – Include full and half joints where – M = degree of freedom or mobility – L = number of links – J1 = number of 1 DOF (full) joints – J2 = number of 2 DOF (half) joints   21213 JJLM 
  • Kinematics Fundamentals
  • Kinematics Fundamentals
  • Kinematics Fundamentals • Mechanisms and Structures – The DOF of an assembly of links completely predicts its character • If the DOF is positive→ mechanism • If the DOF is zero→ structure • If the DOF is negative → preloaded structure
  • Kinematics Fundamentals • Number Synthesis – The determination of the number and order of links and joints necessary to produce motion of a particular DOF
  • Kinematics Fundamentals • Paradoxes
  • Kinematics Fundamentals • Isomers
  • Kinematics Fundamentals • Linkage Transformation – Revolute joints in any loop can be replaced by prismatic joints with no change in DOF of the mechanism, provided that at least two revolute joints remain in the loop
  • Kinematics Fundamentals • Linkage Transformation – Any full joint can be replaced by a half joint, but this will increase the DOF by one – Removal of a link will reduce the DOF by one – The combination of rules 2 and 3 above will keep the original DOF unchanged
  • Kinematics Fundamentals • Linkage Transformation
  • Kinematics Fundamentals • Linkage Transformation – Any ternary or higher–order link can be partially shrunk to a lower–order link by coalescing nodes. This will create a multiple but will not change the DOF at the mechanism
  • Kinematics Fundamentals • Linkage Transformation – Complete shrinkage of a higher-order link is equivalent to its removal. A multiple joint will be created, and the DOF will be reduced
  • Kinematics Fundamentals • Intermittent Motion – Is a sequence of motions and dwells • Dwell; is a period in which the output link remains stationary while the input link continues to move • Geneva Mechanism
  • Kinematics Fundamentals • Intermittent Motion • Ratchet and Pawl
  • Kinematics Fundamentals • Intermittent Motion • Linear Geneva Mechanism
  • Kinematics Fundamentals • Inversion – An inversion is created by grounding a different link in the kinematic chain
  • Kinematics Fundamentals
  • Kinematics Fundamentals • Grashof Condition – Is a simple relationship that predicts the rotation behavior or rotatability of a four linkage’s inversion based only on the link lengths • S = length of shorter link • L=length of longest link • P=length of one remaining link • Q=length of the other remaining link QPLS 
  • Kinematics Fundamentals • Grashof Condition – If the inequality is true, at least one link will be capable of making a full revolution with respect to the ground plane(Class I) – If not true, then the linkage is non-Grashof and no link will be capable of a complete revolution relative to any other link (Class II) QPLS 
  • Kinematics Fundamentals • Grashof Condition – For the class I case: S+L< P+Q • Ground either adjacent to the shortest link and you get a crank-rocker • Ground the shortest link and you will get a double-crank • Ground the link opposite the shortest and you will get a Grashof double-rocker
  • Kinematics Fundamentals • Grashof Condition – For the Class II case: S+L> P+Q • All inversion will be triple-rockers in which no link can fully rotate – For Class III: S+L=P+Q • All inversion will be either double-cranks, or crank-rocker
  • Kinematics Fundamentals
  • Kinematics Fundamentals
  • Kinematics Fundamentals
  • Kinematics Fundamentals • Classification of the Four Linkage – C. Barker developed a classification scheme that allows prediction of the type of motion that can be expected from a fourbar linkage based on the values of its link lengths – Link ratio formation – Letter designation (C), (R) - GCRR
  • Kinematics Fundamentals • Linkages of More Than Four Bars – Geared Fivebar Linkages
  • Kinematics Fundamentals • Linkages of More Than Four Bars – Sixbar Linkages
  • Kinematics Fundamentals • Spring as Links • Compliant Mechanism • Micro Electro-Mechanical Systems (MEMS)
  • Kinematics Fundamentals – Problems
  • Kinematics Fundamentals – Problems
  • Kinematics Fundamentals