Search Here MISC  Parts List  Robot Forum  Chat  Member Pages  Axon MCU  Robot Books  Shop  Contact HARDWARE  Actuators  Batteries  Electronics  Materials  Microcontrollers  Sensors SCIENCE  Robot Journals  Robot Theory  Conferences ROBOT GEARS TUTORIAL Introduction to Gears No good robot can ever be built without gears. As such, a good understanding of how gears affect parameters such as torque and velocity are very important. In this tutorial I will first talk about the basics of gears, how to use them properly along with simple equations, and then I will go into specific types of gears. As with all motors, by looking at the motor datasheet you can determine the output velocity and torque of your motor. But unfortunately for robots, motors commercially available do not normally have a desirable speed to torque ratio (the main exception being servos and high torque motors with built in gearboxes). For example, do you really want your robot wheels to rotate at 10,000 rpm at low torques? In robotics, torque is better than speed. With gears, you will exchange the high velocity with a better torque. This exchange happens with a very simple equation that you can calculate: Torque_Old * Velocity_Old = Torque_New * Velocity_New Torque_Old and Velocity_Old can be found simply by looking up the datasheet of your motor. Then what you need to do is put a desired torque or velocity on the right hand side of the equation. My statics and dynamics tutorials can help you decide on a reasonable torque and/or velocity for your robot. So for example, suppose your motor outputs 3 lb-in torque at 2000rps according to the datasheet, but you only want 300rps. This is what your equation will look like: 3 lb-in * 2000rps = Torque_New * 300rps With highschool algebra you can then determine that your new torque will be 20 lb-in. Now suppose, with the same motor, you need 5 lb-in (minimum force to crush a cat, obviously). But suppose you also need 1500rps minimum velocity. How would you know if the motor is up to spec and can do this? Easy . . . 3 lb-in * 2000rps = 5 lb-in * Velocity_New Velocity_New = 1200rps You now have just determined that at 1200 rps the selected motor is not up to spec. Using the simple equation, you have just saved yourself tons of money on a motor that would have never worked. Designing your robot, and doing all the necessary equations beforehand, will always save you tons of money and time. The gearing ratio is the value at which you change your velocity and torque. Again, it has a very simple equation. The gearing ratio is just a fraction which you multiple your velocity and torque by. Suppose your gearing ratio is 3/1. This would mean you would multiple your torque by 3 and your velocity by the inverse, or 1/3. example; Torque_Old = 10 lb-in, Velocity_Old = 100rps Gearing ratio = 2/3 Torque * 2/3 = 6.7 lb-in Velocity * 3/2 = 150rps Achieving a Particular Gearing Ratio If you wanted a simple gearing ratio of say 2 to 1, you would use two gears, one being twice as big as the other. It isn't really the size as much as the diameter ratio of the two gears. If the diameter of one gear is 3 times bigger than the other gear, you would get a 3/1 (or 1/3) gearing ratio. You can easily figure out the ratio by hand measuring the diameter of the gears you are using. For a much more accurate way to calculate the gearing ratio, calculate the ratio of teeth on the gears. If one gear has 28 teeth and the other has 13, you would have a (28/13=2.15 or 13/28=.46) 2.15 or .46 gearing ratio. I will go into this later, but this is why worm gears have such high gearing ratios. In a worm gear setup, one gear always has a single tooth, while the other has many - a guaranteed huge ratio. Counting teeth will always give you the most exact ratio. Gear Efficiency Unfortunately, by using gears, you lower your input to output power efficiency. This is due to obvious things such as friction, misalignment of pressure angles, lubrication, gear backlash (spacing between meshed gear teeth between two gears) and angular momentum, etc. Different gear setups, different types of gears, different gear materials, and wear and tear on the gear, will all have different efficiencies. The possible combinations are too big to list, so I will give you an estimated efficiency to expect with each gear type below. You can also find a much more exact efficiency by looking up the datasheet on the gears you are using. For example, suppose you use two spur gears, you would typically expect efficiency to be around ~90%. To calculate, multiply that number by your Velocity_New and Torque_New to get your true output velocity and torque. if (from above example) Gearing ratio = 2/3 Torque * 2/3 = 6.7 lb-in Velocity * 3/2 = 150rps then true torque = 6.7 * .9 = 6 lb-in true velocity = 150 * .9 = 135rps effienciency_total = gear_type_efficiency ^ (# of gears - 1) = .9 ^ (29) = 4.7 % If instead you used 5 gears, you would have: effienciency_total = .9 ^ (4) = 65.6 % radius_gear1 * torque_gear1 = radius_gear2 * torque_gear2 In this example, what minimum torque does the motor need to pull the weight up? writing down the equations: torque_motor * radius_gear1 = torque_gear2 * radius_gear2 torque_gear2 * radius_gear2 = torque_gear3 * radius_gear3 torque_gear3 * radius_gear3 = weight * radius_gear3 simplifying, we get: torque_motor * radius_gear1 = weight * radius_gear3 so therefore the minimum required motor torque is torque_motor = weight * radius_gear3 / radius_gear1 Now what if you wanted the weight to lift at 2 feet/sec. What rotations per second and direction must the motor rotate at? writing down the equations: rps_motor * radius_gear1 = rps_gear2 * radius_gear2 rps_gear2 = rps_gear3 rps_gear3 * 2*pi*radius_gear3 = velocity_weight simplifying, we get: rps_motor * radius_gear1 = rps_gear3 * radius_gear2 or rps_motor * radius_gear1 = velocity_weight / (2*pi*radius_gear3) * radius_gear2 so therefore the required motor rps is rps_motor = 2 ft/sec * radius_gear2 / (2*pi*radius_gear3 * radius_gear1) The pitch diameter is as shown. To calculate the pitch, simply use this equation: Pitch = # teeth / pitch circle diameter (in inches) For example, a gear with 72 teeth and a 1.5" pitch diameter is 48 Pitch. Gears that mesh must both have the same pitch and pressure angle (usually 20 degrees). Note: The efficiencies listed are only typical. Because of many other factors could be present, the listed efficiencies should only be used as a guide. Often manufacturers will give you expected efficiencies in the datasheets for their gears. Remember, wear and lubrication will also dramatically affect gear efficiencies. Worm Gears (~70% efficiency) Worm gears have a very high gearing ratio. To mathematically calculate, consider the worm gear as a single tooth. Another advantage to the worm gear is that it is not back-drivable. What this means is only your motor can rotate the main gear, so things like gravity or counter forces will not cause any rotation. This is good say if you have a robot arm holding something heavy, and you don't want to waste power on holding torque. The efficiency is low, but lubrication really helps. More Information If you wish for an even more in-depth tutorial about gear selection, you can find it in this advanced gear selection tutorial. I didn't write it, but it's easy to follow and understand. Where can you buy gears? Check my robot parts list and the ad window at the top right of this page for links. 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