Using Gear Ratios with the V5 Motor

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 to customize power transfer, increase torque, or increase speed. This can be done by assembling two or more gears together on drive shafts so that the teeth of the gears intermesh. A motor will power the drive shaft of one of the gears.

Gear Ratios

Simple gear ratios use only one gear per driveshaft. The gear that provides the power, or input, is called a driving gear and the gear that is being turned, or responsible for the output, is called the driven gear. The gear ratio is calculated by using the following formula:

• Torque: The rotational force that the motor can apply to the robot’s components.
• Speed: Rotational speed is how fast an object is spinning.
• Power Transfer: The process of transmitting energy from the motor to the various parts of the robot to drive the gears, wheels, or other mechanical components.

1:1 Gear Ratio

A 1:1 Gear Ratio means that the driving gear makes one revolution to make the driven gear complete one revolution. This gear ratio provides the following benefits:

• Balanced Speed and Torque: Because the ratio between the driving gear and the driven gear is equal, there is no change in speed or torque between the two gears. This balance is ideal for applications where the motor’s native performance is sufficient.
• Direct Power Transfer: This gear ratio ensures that the power generated by the motor is directly transferred to the driven component without any loss.
• Simplified Design: A 1:1 gear ratio simplifies the mechanical design of the robot, making the design and building process more straightforward.
• Predictable Performance: Since the input and output speeds are identical, the performance of the robot is more predictable. This can be advantageous for tasks where consistent performance is required, or where task timing is crucial.

The graphic below displays an example of a 1:1 Gear Ratio. The driving gear and the driven gear have the same number of teeth (60T). The motor rotates the 60T driving gear once to make the 60T driven gear complete one revolution.

5:1 Gear Ratio

A 5:1 Gear Ratio means that the driving gear must make five revolutions to make the driven gear complete one revolution. This gear ratio provides the following benefits:

• Increased Torque: Torque is the rotational force that the motor can apply to the robot’s components. By increasing the torque, a robot can handle heavier loads and perform tasks that require more force, such as lifting and pushing objects. The driving gear has fewer teeth than the driven gear, causing the torque output to be 5 times as much while the speed output is only 1/5.
• Reduced Speed: While the torque is increased, the speed of the driven gear is reduced. Reduction in speed is beneficial for tasks that require more control and precision.
• Improved Motor Efficiency: A higher gear ratio allows the motor to run more efficiently. This gear ratio can reduce wear on the motor and extend the motor’s lifespan.
• Customization for Specific Tasks: This gear ratio can be integrated with a larger gear system allowing customization of the robot’s performance characteristics.

1:5 Gear Ratio

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 once, the 12T driven gear rotates five (5) times. 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.

Explore the following graphic to view each angle of a 1:5 gear ratio.

Gear Train

A gear train consists of a series of gears that transmit motion and power from one part of the robot to another. Gear trains modify the speed, torque, and direction of rotational motion. Gear trains consist of gears with teeth that mesh together to transmit motion; shafts that hold the gears in place and enable them to rotate; and shaft collars that help to hold all components in place. Functions of a gear train include the following:

• Speed Adjustment: Gear trains increase or decrease rotational speed; a smaller driving gear meshing with a larger driven gear reduces the speed but increases torque, while a larger driving gear meshing with a smaller driven gear increases speed but reduces torque.

Gear trains are used to rotate wheels that are not connected to a motor.

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.

For more information, help, and tips, check out the many resources at VEX Professional Development Plus

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