Kinematics

From MTE 321

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Machine and Mechanisms

A machine uses mechanisms to aid in its function to produce desired motion
A machine is a collection of mechanisms arranged to transmit forces and do work

Kinematics: The study of the geometric aspects of motion.

Position

Calculating the position vector

We calculate position using a vector with some origin as a reference. We’ve been doing this for years so not much to say here, I’ll give the equations anyways…

$R_A=\sqrt{R_x^2+R_y^2}$
$\theta =\arctan \left(\frac{Ry}{R_x}\right)$
We can also transform this polar representation to rectangular form like how we do in Complex Numbers.

Displacement

Displacement

The difference between an initial and final position of a point (change in position).
The magnitude of displacement is path length.

$\overrightarrow{R_{BA}}=\overrightarrow{R_B}-\overrightarrow{R_A}$

Pure Translation

• Is rectilinear or curvilinear:
  • All points moving in straight or curved lines

Pure Rotation

• All particles of a body move along circular paths in planes perpendicular to the axis of rotation

General Plane Motion

• The body undergoes translation and rotation
• Translation occurs within a plane and rotation happens perpendicular to the axis of rotation

Degrees of Freedom

• The number of independent parameters needed to define a systems position in space

Linkages

• The basic building blocks of all mechanisms
• Made of links with joints and nodes

Joints

• Joins are a connection between two or more nodes at the nodes
• Joints are classified by:
  • The type of contact between elements
  • Number of degrees of freedom
  • Physical closure
  • Number of links joined
  • The degree of freedom is one less than the number of links joined

Crank

• A link that makes a complete revolution and is pivoted to the ground

Drawing Kinematic Diagrams

1. Identify frame
2. Identify other links
3. Identify joints and types of joints
4. Identify points of interest