Spring Elements

Spring elements are physical objects whose deformation under forces cannot be treated as negligible.

Coil Spring

A translatory or coil spring has a free length, $L$. When a spring is compressed or stretched, it exerts a restoring force that opposes the compression or extension. This can be examined under the linear force-deflection model:

$$f=kx$$

where $f$ is the restoring force, $x$ is the compression or extension distance (change in length from free length), and $k$ is the spring constant. This is also known as Hooke’s Law.

Torsional Spring

A torsional spring refers to an element that resists with an opposing torque when twisted. This behavior is expressed by:

$$T=k_T\theta$$

where $\theta$ is the net angular twist in the element, $T$ is the torque causing the twist, and $k_T$ is the torsional spring constant. We say $\theta =0$ is the spring position where there is no torque; this is analogous to the free length.

The methods of calculation for the torsional spring constant is shown above.

Spring Constants