# Activity 113 Gears VEXIntroductionYou Do Not

Activity 1.1.3 Gears - VEX

Introduction

You do not have to look far to see gears. You might not think of an object such as a computer as having a lot of moving parts, but the CD tray on your computer is likely controlled by gears. A traditional watch is full of gears. The watch has one source of power or input that must move multiple hands continuously and at different speeds. Some watches also keep track of the day of the month. This may be low-tech by today’s standards, but imagine the challenge of choosing just the right gears to keep a watch synchronized. In a watch the gears are used to manipulate rotational speed. Gears are also used in many applications to control torque and rotational direction. Equipment

VEX POE kit gears and support pieces

Calculator

Procedure

In this activity you will learn about gear ratios and how they affect speed and torque within a system. You will also construct simple and compound gear systems. Functions of Gears

Gears change the speed of rotation.

Gears change the direction of rotation.

Gears change torque values.

Gear Ratios

By joining together two or more gears of different sizes, both the speed and the torque are changed from the input gear to the output gear. The larger gear within a system will always move slower and have more torque than the smaller gear. Gear Ratio (GR) is a comparison between the driver gear, also called the input (connected to the power source), and the gear being driven, or the output. Below are four ways to determine the gear ratio in figure 1.

Method 1: The gear ratio can be determined by counting the number of teeth on each gear. The ratio is expressed by dividing the number of teeth on the output gear (nout) by the number of teeth on the input gear (nin).

Gear ratios are often expressed using a colon. In this example the ratio is 2:1 (pronounced two to one). The gear ratio of 2:1 indicates that the driver gear is half the size of the driven gear, and that the driver gear will make two revolutions for every one made by the driven gear.

Method 2: The gear ratio can be determined using the diameter of each gear. Assume that the diameter of gear A is 2.5 in. (din), and the diameter of gear B is 5 in. (dout).

Method 3: The gear ratio can be determined by recording and comparing the angular velocity or speed at which each gear is turning. The lower case Greek letter ω is used to represent angular velocity. A common way to measure angular velocity is using revolutions per minute (rpm). Assume that the rpm of the input gear is 446 rpm and the rpm of the output gear is 223 rpm.

Method 4: The gear ratio can be determined by recording the torque at each gear. Divide the torque at the output gear (τout) by the torque at the input gear (τint). A common way to measure torque is to use foot pounds (ft·lb). Assume that the torque force at the driver gear is 4 ft·lb and the force at the driven wheel is 8 ft·lb of torque.

The above equations all solve for the gear ratio of the driver gear to the driven gear. Based upon these formulas, the following is true.

Solving for Speed and Torque

In most applications you will know the speed and torque provided by your driver or input gear. You will mesh another gear to achieve a specific output speed or output torque to accomplish a task. Below are some examples that illustrate this.

Example 1: A motor is driving an axle with a 6.0 in. diameter drive gear. The speed of the motor is 20. rpm. A gear must be attached that increases the speed to 100. rpm. What size diameter should the attached gear be?

Example 2: A motor is driving an axle with a 30 teeth drive gear. You know that the maximum output torque of the motor is only 90. ft·lb. A gear must be attached that will increase the torque force to 300. ft·lb in order to lift a heavy object. How many teeth should the attached gear have?

Gear Trains

A gear train consists of two or more gears assembled in order to transfer energy...

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