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GEAR RATIO:

The gear ratio is the relationship between the number of teeth on two gears that are meshed or two sprockets connected with a common roller chain, or the circumferences of two pulleys connected with a drive belt.
Since the number of teeth is also proportional to the circumference of the gear wheel (the bigger the wheel the more teeth it has) the gear ratio can also be expressed as the relationship between the circumferences of both wheels (where d is the diameter of the smaller wheel and D is the diameter of the larger wheel):

Since the diameter is equal to twice the radius;

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GEARS:

Gears are mechanical devices that transmit power and motion between axes. There are a number of different gear types.

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SPUR GEARS:

Spur gears are straight-toothed gears with radial teeth that transmit power and motion between parallel axes. They are widely used for speed reduction or increase, torque multiplication, resolution, and accuracy enhancement for positioning systems.

Gears mate or mesh via teeth with very specific geometry. It is important to consider pitch when searching for spur gears.

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HELICAL GEARS:

Helical gears are circular gears whose teeth curve along a helical path. Helical-toothed gears transmit power and motion between parallel axes (opposite hand) or right-angle axes (same-hand). Helical gears may be anti-backlash, meaning they have a mechanical assist such as a spring to take up any play between meshing gear teeth, thus avoiding backlash when gear direction changes.

Important parameters to consider when specifying helical gears include number of teeth, pitch diameter, face or tooth width, and outside diameter. The number of teeth, along with desired pitch diameter, will dictate the pitch of the gear. The face width is width of the teeth. Gear hand direction and pressure angle are also important to consider. Helical gears have a right or left hand specification, which describes the direction of tooth curve. Helical gears of opposite hand (one right and one left) will mesh for parallel-axis power transmission. Same-hand pairs will mesh for perpendicular or off-axis power transmission, depending on the helix angle. Gears must have the same pressure angle to mesh.

Right Hand angle of the teeth

Left Hand angle of the teeth

We can check visually the angle of the teeth.For this purpose ,we Place the gear lying flat on a table, if the teeth go up to the right direction, the angle of the teeth is a Right Hand one, if the teeth go up to the left direction, the angle of the teeth is a Left Hand one.