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. Images from Tiptop Industry Co., Ltd. Image from Northern Tool + Equipment Catalog Co.
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 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 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 Each type of joint imposes a certain number constraints (i.e., takes away a certain number of DOF from mechanism): Type of Joint Revolute variables Planar Mechanism DOF DOF removed Prismatic Cam Gear
MAE 342 Dynamics of Machines 8 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 e) Spherical joint (G) Spherical motion f) Flat joint (F) Planar motion Figure from Unigraphics on-line documentation.
MAE 342 Dynamics of Machines 9 Type of Joint Revolute variables Spatial Mechanism DOF DOF removed Prismatic Screw Cylinderical Spherical Flat/Planar
MAE 342 Dynamics of Machines 10 Kutzbach Criteria for mobility (m) of: planar mechanisms: m = spatial mechanisms: m = where:
MAE 342 Dynamics of Machines 11 In Kutzbach criteria a) If m > 0 b) If m = 0 c) if m < 0
MAE 342 Dynamics of Machines 12 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 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 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