Study guide: Mechanism Kinematic Analysis

📋 Course Outline

1. Mechanics and Mechanism Definitions
2. External System Analysis
3. Degrees of Freedom and Motion
4. Links and Joint Characterization
5. Kinematic Analysis Procedure
6. Kinematic Diagram Conventions

📖 1. Mechanics and Mechanism Definitions

🔑 Key Concepts & Definitions

• Mechanism: A combination of rigid and/or flexible bodies connected to do work with definite constrained relative motions between them.
• Machine: An arrangement of parts and/or mechanisms for doing work, with constrained relative motions between its parts.
• Kinematics: Studies the geometry of motion without reference to the forces causing it, including position, displacement, rotation, speed, velocity, and acceleration.
• Structure: The same definition as a mechanism, but it does not do work and its parts have no relative motion.
• Kinetics: Relates the action of forces on bodies to their resulting motions.

📝 Essential Points

• Dynamics combines kinematics and kinetics and deals with the action of forces on bodies in motion.

💡 Memory Hook

Kinematics describes motion; kinetics connects forces to motion.

📖 2. External System Analysis

★ Must-know

• External analysis identifies and studies the environment outside the boundaries of the object of interest.

• External analysis identifies:

  • the global function
  • the environment
  • the study boundaries
  • the input/output parameters
  • the operating phases

Further detail

• In the door example, the input parameters are scroll-wheel rotation generated by door displacement and the screw-height setting at the trigger moment; the output is screw translation that activates the contactor.

• In the door example, phase 1 is door displacement by hydraulic cylinders until a signal is given to the conductor, and phase 2 is maintenance adjustment of screw height to change the trigger moment and resulting kinematics.

💡 Memory Hook

From the environment, set boundaries, identify inputs and outputs, then operating phases.

📖 3. Degrees of Freedom and Motion

🔑 Key Concepts & Definitions

• Degree of freedom: The number of independent parameters needed to define its position uniquely at any instant.
• Pure translation: Motion in which all points on a body follow curvilinear paths without a change in the body's angular orientation.
• Pure rotation: Motion in which one point of the body is the center of rotation and all other points rotate about it.
• Complex motion: Combines rotation and translation, changing both the linear position and angular orientation of any imagined line on the body.

📝 Essential Points

• A rigid object in three-dimensional space has six degrees of freedom: three translations and three rotations.

💡 Memory Hook

Translation changes position without orientation; rotation changes orientation about a center.

📖 4. Links and Joint Characterization

🔑 Key Concepts & Definitions

• Link: An individual mechanism part considered rigid and connected to other links to transmit motion and forces.
• Joint: A connection between two or more links that allows some motion between the connected links.

★ Must-know

📌 A joint's degree of freedom is the number of non-zero twist components describing possible relative motions, while its degree of linkage is the number of non-zero wrench components describing transmittable efforts; the course states that their sum is six when dissipated internal power is neglected.

Further detail

📌 A simple link contains two joints, whereas a complex link contains more than two joints.

• The order of a link is the number of joints, or nodes, to which that link is connected.

• The ideal-joint assumptions are: solids in relative motion are undeformable, functional surfaces are geometrically perfect and conserved, surface positioning is perfect, friction between parts is neglected

📖 5. Kinematic Analysis Procedure

★ Must-know

• 🔄 Kinematic analysis proceeds by: defining the operating phase, identifying the input and output, defining groups, recording non-movement relationships between parts in a graph, identifying relative motions and joints between each pair of groups

Further detail

• 🔄 To complete the link graph: consider two groups at a time, determine their possible relative movements, choose the corresponding joint, connect groups with relative motion using thick lines labeled with the joint

• The twist of a moving part relative to a frame describes up to three translational velocity components along x, y, and z and three angular velocity components about x, y, and z.

• A wrench describes the forces and torques transmittable between parts, with force components along x, y, and z and torque components about x, y, and z.

• The course names these joint types:

  • complete or embedding
  • cylindrical
  • turning or revolute
  • sliding
  • helical
  • planar
  • spherical
  • edge slider
  • sphere groove
  • point slider

💡 Memory Hook

Phase → inputs and outputs → groups → relative motions and joints.

📖 6. Kinematic Diagram Conventions

★ Must-know

📌 In a kinematic diagram, thick lines represent joints and interactions between groups, not the thickness or shape of parts.

• A kinematic diagram follows identification of the link graph and should preserve the mechanism's form, positions, and orientations.

Further detail

📌 Colours must be used in a kinematic diagram to differentiate the groups and joint representations.