MECH0414 Introduction to Multibody Dynamics Concepts of Kinematics PDF, 1/2024

MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.1 Concepts of Kinematics Mechanical Engineering-1/2024 MECH0414 : Introduction to Multibody Dynamics Conc...

MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.1 Concepts of Kinematics Mechanical Engineering-1/2024 MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.2 Concept of Kinematics : 1. Systems of rigid bodies/Linkage (Bodies or Components) 2. Kinematics diagram 3. Joint types or Kinematics pair 4. Degrees of freedom (DOF) or Mobility 5. Motion (2D or Plane motion) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.3 1.Systems of rigid bodies/Linkage (Bodies or Components) Multi-body system (Dynamics/Motion) (Systems of bodies or Components) Focus Geometry of linkage mechanisms Figure 2.1 Multi-body system (Bodies or Components) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.4 2. Kinematics diagram Difficult to visualize Body, Link, Component Focus Dimensions Table 2.1 Kinematic Representation (Stripped-down) Component Typical Form Kinematic Simple Link (straight) Simple Link (Curve) Complex Link MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.5 2. Kinematics diagram (Cont.) Table 2.1 Kinematic Representation (Cont.) Component Typical Form Kinematic Pin joint Slider joint Cam joint MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.6 2. Kinematics diagram (Cont.) Table 2.1 Kinematic Representation (Cont.) Component Typical Form Kinematic Gear joint MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.7 3. Joint types or Kinematics pair A kinematics chain is defined as: An assembly of links (bodies, components) and joints, interconnected in a way to provide a controlled output motion in response to a supplied input motion. Figure 2.2 Multi-body system (Bodies or Components) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.8 3. Joint types or Kinematics pair (Cont.) A joint is a connection between two or more links (at their nodes), which connection allows some motion, or potential motion, between the connected links. Pin joint / Hinge joint (Lower pairs, R) Slider joint / Piston or Prismatic joint (Lower pairs, P) Cam joint (Higher pairs, RP) Gear joint (Higher pairs, RP) Figure 2.3 Joints (pairs) of various types (Lower pairs and Higher pairs) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.9 3. Joint types or Kinematics pair (Cont.) A joint is a connection between two or more links (at their nodes), which connection allows some motion, or potential motion, between the connected links. Rotating pin (R) Translating slider (P) (a) (b) Second order pin (RR) Rolling (R) or Roll-Slider (RP) (c) (d) Figure 2.4 Joints (pairs) of various types MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.10 3. Joint types or Kinematics pair (Cont.) Helical joint (R) Cylindric joint (RP) (e) (f) Link against plane (RP) Pin in slot (RP) (g) (h) Figure 2.4 Joints (pairs) of various types (Cont.) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.11 3. Joint types or Kinematics pair (Cont.) Figure 2.5 Schematic notation for kinematics diagram MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.12 4. Degrees of freedom (DOF) or Mobility The degree of freedom (DOF) is the number of independent inputs required to precisely position all links of the mechanism with respect to the ground. It can also be defined as the number of actuators needed to operate the mechanism (system of rigid body) Produces: Displacement, Force, Torque Controlled Electrical Hydraulic Pneumatic Figure 2.6 Types of actuators MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.13 4. Degrees of freedom (DOF) or Mobility Multi-body systems Degree of freedom (DOF, M) Gruebler’s equation DOF/M = 3 𝑛 − 1 − 2𝑗𝑝 − 𝑗ℎ Where: n = Total number of links in the mechanism jp = Total number of lower paris (pin, slider)/ one motion jh = Total number of higher paris (cam, gear)/ two motion MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.14 4. Degrees of freedom (DOF) or Mobility (Cont.) Figure 2.7 Degrees of freedom for plane motion of a rigid body MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.15 4. Degrees of freedom (DOF) or Mobility (Cont.) Figure 2.7 Degrees of freedom for plane motion of a rigid body (Cont.) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.16 4. Degrees of freedom (DOF) or Mobility (Cont.) Figure 2.7 Degrees of freedom for plane motion of a rigid body (Cont.) MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.17 Problem1 1). 17 MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.18 Problem1 2). 18 MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.19 Problem1 3). 19 MECH0414 : Introduction to Multibody Dynamics Concept of Kinematics : P.20 Problem1 4). 20