MER035 Lecture 1 Union College Mechanical Engineering MER 312 Dynamics and Kinematics (of Mechanisms) / AT Degree of Freedom No of independent coordinates needed to define position of body How many DO[.]
Degree of Freedom No of independent coordinates needed to define position of body How many DOF does a body in three-space (3-D) have? Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Definitions All of the above contain linkages which consist of: • • Links Joints Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Links A link is a nominally rigid body that possess at least nodes A node is an attachment point to other links via joints Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Links - The order of a link indicates the number of joints to which the link is connected (or the number of nodes per link) There are binary (2 nodes), ternary (3 nodes), and quaternary (4 nodes) links - Can be any shape (not just those shown) -Link order = number of nodes Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Links - Are assumed to be rigid bodies - Have nodes for attachment - Can be any shape (not just those shown) -Link order = number of nodes Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT JOINTS Joints allow DOF between links Union College Mechanical Engineering A joint is a connection between two or more links at their nodes, which allows motion to occur between the links A pivot is a joint that allows rotary motion, A slider is a joint that allows linear motion MER 312: Dynamics and Kinematics (of Mechanisms) / AT JOINTS Joints allow DOF between links Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT 2.5: Determining DOF or Mobility Joints Reduce System DOF Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT 2.5: Determining DOF or Mobility Joints Reduce System DOF Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Kinematics Diagrams Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Determining Mobility or DOF Gruebler & Kutzbach Equations Gruebler’s Equation is the most commonly used equation for evaluating simple linkages Kutzbach’s equation is modified Gruebler’s Equation that takes into consideration full (1 DOF) and half (2 DOF) joints Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Determining Mobility or DOF Grubler & Kutzbach Equations Lower pairs (first order joints) or full-joints (counts as J = in Gruebler’s Equation) have one degree of freedom (only one motion can occur): –- Revolute (R): Also called a pin joint or a pivot, take care to ensure that the axle member is firmly anchored in one link, and bearing clearance is present in the other link , washers make great thrust bearings, snap rings keep it all together • A rolling contact joint also counts as a one-degree-of-freedom revolute joint - Prismatic (P): Also called a slider or sliding joint, beware Saint-Venant! - Helical (H): Also called a screw, beware of thread strength, friction and efficiency Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Determining Mobility or DOF Gruebler & Kutzbach Equations Joints: Multiple Degree-of-Freedom • Lower Pair joints with multiple degrees of freedom: – Cylindrical (C) DOF • A multiple-joint (J = 2) – Spherical (S) DOF A multiple-joint not used in planar mechanisms (J = 3) – Planar (F) DOF • A multiple-joint (J = 3) Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Determining Mobility or DOF Gruebler & Kutzbach Equations Joints: Higher Pair Multiple Degree-of-Freedom • Higher Pair joints with multiple degrees of freedom: – Link against a plane and a force is required to keep the joint closed (force closed) – A half-joint (J = in Kutzbach’s equation) • The link may also be pressed against a rotating cam to create oscillating motion – Pin-in-slot • Geometry keeps the joint closed (form closed) (Slide and pin) – A multiple-joint (J = in Gruebler’s equation) – Second order pin joint, links joined, 2-DOF • A multiple-joint (J = in Gruebler’s equation) Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Kinematics Diagrams Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Applying Mobility Equations - M = (L-1) –2(J1) – J2 = 3(8-1) –2(10) – = Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Applying Mobility Equations - M = (L-1) –2(J1) – J2 = 3(6-1) –2(7) – = Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT ... Kinematics (of Mechanisms) / AT Determining Mobility or DOF Gruebler & Kutzbach Equations Joints: Multiple Degree- of- Freedom • Lower Pair joints with multiple degrees of freedom: – Cylindrical (C) DOF. .. Mechanisms) / AT Determining Mobility or DOF Gruebler & Kutzbach Equations Joints: Higher Pair Multiple Degree- of- Freedom • Higher Pair joints with multiple degrees of freedom: – Link against a plane... Joints Reduce System DOF Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT 2.5: Determining DOF or Mobility Joints Reduce System DOF Union College Mechanical