MAE 342 – Dynamics of Machines
Types of Mechanisms
Classification of Mechanisms by type and mobility MAE 342 – Dynamics of Machines 2
Planar, Spherical and Spatial Mechanisms • Planar Mechanisms: all points on each part move only in .
Image from Technische Universität Ilmenau.
Image from Northern Tool + Equipment Catalog Co. Images from Tiptop Industry Co., Ltd. MAE 342 – Dynamics of Machines 3
Planar, Spherical and Spatial Mechanisms • Spherical Mechanisms: all points on each part move only in .
Image from Maarten Steurbaut.
Images from the Laboratory for the Analysis and Synthesis of Spatial Movement.
Images from Laboratoire de robotique, Université Laval. MAE 342 – Dynamics of Machines 4
Planar, Spherical and Spatial Mechanisms
• Spatial Mechanisms: points on each part can move in any direction in 3-dimensional space.
Image from the Kinematic Models for Design Digital Library, Cornell University.
Image from www.robots.com. Image from Slika
Image from the Special Session on Computer Aided Linkage Synthesis, ASME DETC 2002. MAE 342 – Dynamics of Machines 5 Mobility • Degrees of freedom (DOF) is: the number of independent controls needed to position a body. Mathematically it is the number of independent variables needed to specify the position of a body.
A planar body has ___ DOF.
A spherical body has ___ DOF.
A spatial body has ___ DOF. MAE 342 – Dynamics of Machines 6 Mobility
• Mobility is: the number of degrees of freedom of a mechanism.
If the number of planar bodies is n (and there are no joints) the mobility is ______.
If one of the bodies is fixed, the mobility is ______.
If the number of spatial bodies is n (and there are no joints) the mobility is ______.
If one of the bodies is fixed, the mobility is ______. MAE 342 – Dynamics of Machines 7 Mobility • Each type of joint imposes a certain number constraints (i.e., takes away a certain number of DOF from mechanism) : Planar Mechanism Type of Joint variables DOF DOF removed Revolute
Prismatic
Cam
Gear MAE 342 – Dynamics of Machines 8 Mobility
Figure from Uicker et al., Theory of Machines and Mechanisms a) Revolute joint (R) – Circular motion b) Prismatic joint (P) – Rectilinear motion c) Screw joint (S) – Helical motion d) Cylindrical joint (C) – Cylindrical motion Figure from Unigraphics on-line documentation. e) Spherical joint (G) – Spherical motion f) Flat joint (F) – Planar motion MAE 342 – Dynamics of Machines 9 Mobility Spatial Mechanism Type of Joint variables DOF DOF removed
Revolute
Prismatic
Screw
Cylinderical
Spherical
Flat/Planar MAE 342 – Dynamics of Machines 10 Mobility • “Kutzbach Criteria” for mobility ( m) of:
planar mechanisms: m =
spatial mechanisms: m =
where: MAE 342 – Dynamics of Machines 11 Mobility • In Kutzbach criteria a) If m > 0
b) If m = 0
c) if m < 0 MAE 342 – Dynamics of Machines 12 Mobility • What is the mobility in these examples?
a)
b)
c)
d)
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003 MAE 342 – Dynamics of Machines 13 Mobility • What is the mobility in these examples?
a)
b)
c)
d)
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003 MAE 342 – Dynamics of Machines 14 Mobility • Exceptions to the rule!
Certain geometric conditions
Different parts of a linkage can have different mobilities. MAE 342 – Dynamics of Machines 15
Torfason’s Classification of Mechanisms • Snap-Action Mechanisms • Linear Actuators • Fine Adjustments • Clamping Mechanisms • Locational Devices • Ratchets and Escapements • Indexing Mechanisms • Swinging or Rocking Mechanisms • Reciprocating Mechanisms • Reversing Mechanisms • Couplings and Connectors • Stop, Pause, and Hesitation Mechanisms • Curve Generators • Straight-Line Generators • … MAE 342 – Dynamics of Machines 16 Kinematic Inversion • You can pick different links to be the fixed link – this is “kinematic inversion”
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003 MAE 342 – Dynamics of Machines 17 Grashof’s Law • In a four bar linkage, if you want to be able to sit on one link and have some other link rotate 360° relative to you , then:
where: s is the length of:
l is the length of:
p, q are the lengths of: MAE 342 – Dynamics of Machines 18 Grashof’s Law
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003