# 4.3. Mechanical Behavior¶

This section is about encoding behavior in machines, where behavior is loosely interpreted as the response of a machine to a varying environment in order to achieve an implicit goal. At the limit, this encompasses all of robotics. However, machines can achieve their smarts through many means including physical form which passively interacts with the world, mechanical action which responds to forces, and computational models which span complexity from simple reflex reactivity to detailed world models.

## 4.3.1. Takeaway Lessons¶

Machines have parts which move relative to each other; the elements or surfaces where relative motion occurs are bearings and serve the functions of controlling relative motion and friction. These can be rolling-contact devices such as ball bearings in which small steel balls roll between concentric surfaces, but many common bearings are plain bearings in which two surfaces simply slide over each other. Even a book sliding on a table can be considered to be using a planar sliding bearing formed by the book jacket and the smooth table: the shape constrains motion to the plane, and the smooth materials limit friction.

The common types of bearing components we will use are bushings and ball bearings. Bushings are plain bearings made from a low-friction material such as bronze.

The key principles of shaft bearing design are to consider the radial force acting perpendicular to the shaft, the axial force (or thrust) acting along the shaft, the bending moments induced by the loads, and the torque carried by the shaft.

Most ball bearings have limits on the moments they can support, so a good rule of thumb is to always use bearings in pairs such that the shaft bending moments are counted by radial forces.

Common ball bearings can support higher radial loads than axial loads. Thrust bearings are specifically designed to carry axial loads, such as in a turntable.

Electric motors are generally high-speed low-torque devices. Actuating a mechanism almost always requires some form of transmission to reduce speed and increase torque to match a load.

For our purposes, transmissions will be built from rollers, timing pulleys and belts, winches and cable drives, and gears. These are mechanisms with constant-ratio transfer functions in which an input to output velocities have a fixed ratio.

In general, any mechanism with a transfer function between input and output can act as a type of transmission. Structures with non-constant ratios include levers, cams, and linkages.

Gear tooth design comes down to a straighforward idea: find compatible shapes which interact to produce a constant velocity ratio from input to output. The classic involute gear tooth shape essentially creates the simple input-output behavior of two non-slipping rollers, but with the increased load capacity of face contact instead of frictional contact.

In practice, gears have many problems: the teeth must slide across each other, creating noise and friction; involute teeth induce forces which press the gears apart; high-torque metal gears are often expensive precision parts. However, low-cost gears can be laser-cut and careful attention to shaft stiffness can manage tooth pressure forces.

Other common design problems we will face: attaching gears and pulleys to shafts; mounting motors and actuators; attaching feedback sensors; using bearings to reduce friction; translating rotational to linear motion; building rigid structures; designing for assembly; creating 3D structures from flat parts; creating snap-fit and locking features; designing using standard parts and fasteners.