How to Use Simple Gear Ratios

The VEX EDR system has two types of spur gears, the Gear Kit and the High Strength Gear Kit (please see How to Select a Spur Gear). These gears can be assembled for power transfer, to increase torque, or to increase speed. This can be done by assembling two or more gears together on drive shafts so their teeth intermesh. A motor will power one of the gears’ drive shaft.

Simple Gear Ratios

Simple gear ratios use only one gear per driveshaft and can be used for power transfer, increasing torque, or increasing speed. The gear which provides the power or input is called a driving gear and the gear which is being turned or output is called the driven gear.

Power Transfer - With this type of gear ratio the objective is to transfer the power from one location to another, such as from a motor to a wheel which is not directly attached to the motor. The driving gear and the driven gear have the same number of teeth. For example, the motor drives a 60 tooth gear (60T) to a driven 60T gear on a wheel. The motor rotates the 60T driving gear once rotating the 60T driven gear on the wheel once. This is known as a 1:1 ratio.

Increase Torque (low speed) - With this type of gear ratio, the objective is to increase the torque from the motor such as from a motor to an arm. The driving gear has fewer teeth than the driven gear. For example, if a motor drives a 12T gear to a driven 60T gear on an arm, the 12T driving gear has to rotate 5 times to rotate the 60T driven gear once. This is known as a 5:1 ratio. The torque output is 5 times as much, however, the speed output is only 1/5.

Increase Speed (high speed) - With this type of gear ratio the objective is to increase the speed from the motor, such as from a motor to a wheel. The driving gear has more teeth than the driven gear. For example, if a motor drives a 60T gear to a driven 12T gear on a wheel, when the 60T driving gear rotates 5 times, the 12T driven gear rotates. This is known as a 1:5 gear ratio. In this case, the speed output is 5/1 times as much, however, the torque output is 1/5.

Special Notes

  • The ratios for sprocket and chain systems work the same way as gear ratios. Sprocket and chain systems have the advantage that the sprockets can be placed at multiple distances apart because they are connected by a chain. However, the chain links can break with less force than a tooth can break on a High Strength Gear. Either type of breakage will need to be repaired in order for the robot to be fully functional.
  • Any number of any size gears can be placed between the driving gear and the driven gear in a simple gear ratio and it will not change the gear ratio. For example, a 12T gear drives a 36T gear which drives a 60T driven gear, the gear ratio is still 5:1, the same as if the 60T gear was driven directly by the 12T gear.

Speed

Rotational speed is how fast an object is spinning. For example, a V5 Smart Motor’s shaft socket could be spinning 100 revolutions per minute or 100 RPM. As explained above, if a 5:1 gear ratio is used, a 60 tooth driving gear is turned by the motor’s shaft and then it turns a 12 tooth driven gear, the 12 tooth gear will rotate at a speed 5 times faster. Using the example above, the 12 tooth gear will then be spinning at 500 RPM compared to the 100 RPM of the motor’s shaft. If a 1:5 gear ratio is used, a 12 tooth driving gear is turned by the motor’s shaft and then it turns a 60 tooth driven gear, the 60 tooth gear will rotate at a speed 1/5 as fast. Using the example above again, the 60 tooth gear will be spinning at 20 RPM compared to the 100 RPM of the motor shaft. 

So why wouldn’t the fastest gear ratio possible always be used? It would seem the faster a robot could move the more competitive it would be. The first reason is, there is an upper speed at which the functions of a robot can be controlled. For a couple of examples, if the function is the robot driving around, if the wheels spin too fast it may be very difficult to control. If the function is an arm rotating up and down, if it rotates too fast, it may also be difficult to control.

Torque

Torque is the amount of force needed to rotate a load at a distance. Motors have a limited amount of torque. For example, if a V5 Smart motor is producing 1 Nm (Newton meters) of torque, when a 5:1 gear ratio is used the driven 12 tooth gear will output ⅕ the motor’s torque input, the output will be 0.2 Nm and with the 1:5 gear ratio, the 60 tooth gear will output 5 times the motor’s torque input, the output will be 5 Nm. 

Torque is the second reason the fastest gear ratio possible can not always be used when designing a robot. It is possible when an increase speed gear ratio is used to drive the wheels of a robot faster, the gear ratio may exceed the available torque from the motor and the robot will not move as fast or move at all. It is also possible if two robots which have nearly the same design interact, the robot with a lower gear ratio drivetrain will likely be able to push the robot with a higher gear ratio drivetrain because the lower gear ratio robot will have more torque. Another example is, an arm may not rotate even if it is directly attached to a shaft which is inserted into a motor because rotating it may exceed the motor’s available torque. In this case, an increase torque gear ratio needs to be used to increase the output of the motor’s torque and exceed the amount of torque which is required to rotate the arm.

A V5 Smart Motor’s speed and torque can be measured using the Motor Dashboard

Robot Reality

Fortunately, the gear ratios used with the build instructions for the assembly of the V5 ClawBot are sufficient to start designing custom robots. Many drivetrains work well by directly driving the shafts of wheels or track sprockets with the V5 Smart Motor with the green 200 RPM V5 Gear Cartridge. However if a structure in the design such as a tower or game piece intake needs to be placed where a motor is located, a power transfer using sprockets and chain or gears such as explained above can be used. For most arms the 7:1 increase torque gear ratio explained above is sufficient by driving the 12T gear with a 200 RPM motor and attaching an 84T driven gear to the arm. As a competitive advantage becomes more important, finding the “sweet spot” balance between speed and torque becomes more important. This can be accomplished by using a V5 Smart Motor with one of the three available V5 Gear Cartridges (Red:100 RPM, Green:200 RPM, Blue: 600 RPM) and if needed, combining the motor with a gear ratio to increase torque or a gear ratio to increase speed.

Gears and other motion hardware can be purchased at https://www.vexrobotics.com/vexedr/products/motion.