Skip to content
Sahithyan's S1
Sahithyan's S1 — Mechanics

Mechanisms

Mechanism

An assembly of rigid bodies or links designed to obtain a desired motion from an available motion while transmitting appropriate forces and moments. Motion of the links have definite relative motion with other links.

Simple mechanisms

  • Lever
  • Pulley
  • Gear trains
  • Belt and chain drive
  • Four bar linkage

Other complex mechanisms

  • Lock stitch mechanism (used in sewing machine)
  • Geneva mechanism
    Constant rotational motion to intermittent rotational motion. mostly used in watches.
  • Scotch yoke mechanism
    Constant rotational motion to linear motion (vice versa.). Mainly used as valve actuators in high pressure gas pipelines.
  • Slider crank mechanism
    Used in internal combustion engines

Method of instantaneous centre of rotation

  • Find the instantaneous centre of the rotation from known velocities at known points
  • Use the instantaneous centre to find velocities at other points

Kinematic chain

An arbitrary collection of links (forming a closed link) that is capable of relative motion and that can be made into a rigid structure by an additional single link.

Lower and Higher pairs

Lower Pair

Aka. primary pair. A pair of kinematic elements which share a surface of contact.

When a rigid body is constrained by a lower pair, which allows only rotational or sliding movement. It has degree of freedom, and the degrees of freedom are lost.

Some examples:

  • Turning pair
  • Sliding pair
  • Helical thread

Higher Pair

A pair of kinematic elements which share only a line or a point of contact.

When a rigid body is constrained by a higher pair, it has degrees of freedom: translating along the curved surface and turning about the instantaneous contact point.

Gear is an example.

When 2 independent objects are brought together to create a link, some degree of freedom will be lost.

Grubler’s Equation

Suppose kinematic elements are brought together. of them is fixed. The remaining elements have degrees of freedom. Each lower pairs loses degrees of freedom. Each higher pairs loses degree of freedom. For a workable mechanism, resultant degrees of freedom must be .

Here:

  • - degree of freedoms
  • - number of kinematic elements
  • - number of lower pairs
  • - number of higher pairs