> For the complete documentation index, see [llms.txt](https://jamesbrayy.gitbook.io/atar/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jamesbrayy.gitbook.io/atar/engineering/core/mechanisms.md).

# mechanisms

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## key terms

* **backlash**: the small gap or play between mechanical parts, like gears or screws, which causes a slight delay when changing direction.
* **lead**: lead refers to the linear distance a screw thread moves in one complete revolution.
* **machine**: a machine is a device that overcomes a resistance (called the load) by applying a force (called the effort).
* **mechanism**: a mechanism is a system of interconnected components designed to transmit, control, or convert motion and force.
* **pitch**: pitch refers to the distance between repeating features in a linear or rotational system, such as the distance between threads on a screw or teeth on a gear.
* **revolution**: the number of complete 360-degree rotations a gear makes around its central axis.
* **starts**: refers to the number of independent thread helices wrapped around the shaft of a screw.
* **teeth**: the protruding edges around the circumference of a gear that mesh with the teeth of another gear to transmit motion and torque.

## types of motion

* ![](/files/AzwtDUNj9fExAsRMBYNh)

## torque

* torque is rotational equivalent of force
* it is a measure of the rotational force that causes an object to rotate about a pivot point or axis
* it occurs when a perpendicular force is applied at a distance from a pivot point
* the further the force is applied from the pivot point, the greater the torque.

## MA and VR

#### mechanical advantage (MA)

* mechanical advantage is defined as the ratio of the load to the effort.
  * it is calculated with $$\text{MA}=\frac{F\_{load}}{F\_{effort}}$$
* if MA > 1, it has become easier to move the load. the greater the mechanical advantage, the easier it will be to move the load
* if MA < 1, it has become harder to move the load. the smaller the mechanical advantage, the harder it is to move the load.
* if MA is equal to 1, then the effort force is equal to the load force.

#### velocity ratio (VR)

* velocity ratio is defined as the ratio of the distance moved by effort and load in the same time interval.
  * i.e. $$\text{VR}=\frac{d\_{effort}}{d\_{load}}$$
* therefore, it is also a ratio of the speeds between the driver and follower.
  * i.e. $$\text{VR}=\frac{v\_{driver}}{v\_{follower}}$$
* if VR is > 1, then there is a loss of speed and an increase in torque. if the velocity ratio is 2, then the speed has halved but the torque has doubled.
* if VR is < 1, then there is a gain of speed but a decrease in torque. if the velocity ratio is 0.5, then the speed has doubled but the torque has halved.
* if VR is equal to 1, then the speed and torque stays the same.

#### both

* if we assume that there is no energy loss for a system ($$\eta=100%$$), then for a simple machine the mechanical advantage and velocity ratio are equal.
* $$\implies \frac{load}{effort}=\frac{\text{distance moved by effort}}{\text{distance moved by load}}$$

#### velocity calculations

* $$v\_{output} = \frac{v\_{input}}{\text{VR}}$$
* $$v=\frac{s}{t}$$
* $$v=\frac{\text{RPM} \times 2\pi r}{60}$$