Springs are mechanisms that have the capacity to absorb, store and release energy through a change in shape. The most common use for a spring is to return a mechanism to its starting position and/or to add cushioning. Examples of applications that use springs include firearms (triggers), mouse traps, trampolines and car suspensions. The amount of energy generated by the change in shape is governed by Hooke’s Law (within the elastic limitations of the material).
As mentioned above, springs are governed by Hooke's law which is defined by the equation:
F = kx
Where:F is the force
The term “relaxed position” relates to the length of the spring when it is not experiencing any force. As the spring is compressed or extended, the force acting in the opposite direction continues to grow proportionally. Each spring has a maximum force it can withstand as dictated by the manufacturer. Going beyond the maximum compression force will lead to the spring becoming fully compressed and solid. Going beyond the maximum tension force will lead to plastic, or permanent, deformation and/or possibly even fracture.
Different materials have different spring constants (a constant term that defines the way the material responds to force inputs). The spring constant is a function of the material’s properties, coil thickness, and the number of turns in the coil. This figure is often given by the spring manufacturer, but can be found using the following equation:
Where:G is the shear modulus of the material
Many different forms of this mechanism exist including torsion, extension, constant-force, and compression springs. Springs come in a variety of sizes depending on the application.
Figure 1. Springs used in this type of catapult are great examples of extension springs
In the cases of compression and extension springs, the coils are compressed or extended linearly which creates a force that opposes that motion. Once the load is released from the spring it will oscillate linearly back and forth about its “relaxed” position. However, it will not oscillate forever as frictional forces cause a loss of kinetic energy, eventually causing the spring cease motion.
Figure 2. Compression and Extension Springs
Torsion springs act differently than compression or extension springs. The coils of torsion spring appear to be fully compressed with straight ends of the coil sticking out on either side. When one end of the torsion spring is fixed and the other rotated, the coil begins to deform which creates a force opposing that rotation. These springs still obey Hooke’s law; however, the variable x is replaced with ϴ which represents the angle of twist from the equilibrium position (in radians).
Figure 3. Torsion Spring
There is one type of spring that does not obey Hooke’s law: constant force springs. As the name dictates, these mechanisms deliver a near constant force. Constant force springs are thin, rolled sheets of metal with a drum or shaft in the center. The drum or shaft serves to keep the geometry of the coil nearly constant resulting in a nearly constant force since the majority of the force opposing motion is stored in the coil.
Figure 4. Constant Force Spring