The following notes are from: Robotic Systems ECE 401RB Fall 2006 Lecture 8: Actuators Part 2 Chapter 19, G. McComb, and M. Predko, Robot Builder's Bonanza, Third Edition, Mc- Graw Hill, 2006. I. Gears and Gear Reduction Normal running speed of motors is too fast for most robotics applications. And the torque is too weak. Locomotion systems needs motors running from 75 to 150 r/min. For a wheel with 3 inch circumference. - (150 rev/min)*(3 inches/rev)*(1/60 min/sec) = 7.5 inches/sec. What happens when a robot moves too fast? Wheels slip. Runs into walls and people. Cannot process sensor information fast enough. Cannot stay on a line. Cannot stop fast enough (or must also have brakes). Lecture 8, Page 1 of 7
Arms, gripper, mechanisms, and most other mechanical systems need even slower motors. 20 r/min down to 5 or 8 r/min - (5 r/min)*(1/60 min/sec)*(360 degrees/rev) = 30 degrees/sec. Two methods exist to decrease motor speed. Bigger motors Gear reduction practical. - Used cars, bicycles, washing machines, and countless othermotor operated mechanisms. Gears 101 Gears perform two important duties. Make the number of revolutions applied to one gear greater than or lesser than another gear connected to it. Increase or decrease torque. - Depending on how the gears are oriented. - Gears can also serve to transfer force from one place to another. Consider the following figure. The small gear is driven by a motor. For each revolution of the smaller gear, the larger gear makes ½ revolution. - A movement of 15 teeth occurs for both gears. If the small gear turns at 1000 r/min, the larger gear turns at 500 r/min. Gears are like round levers A small amount of torque applied at the edge of a large gear translates into a large amount of force at the shaft. Lecture 8, Page 2 of 7
Like a small amount of force on the long side of a lever translates into a large amount of force on the short side. - Because torque is force times distance. d1*f1=d2*f2 If d2 is less, f2 will be more. This is how gears not only change speed of rotation, but also torque. Consider the above figure - The motor produces a torque on the shaft at the center of the smaller gear. - Which exerts a smaller force on the circumference of that gear and on the larger gear. - But the force on the center of the larger gear is larger. - The distance to the center of the larger gear is twice that of the smaller gear (since it has twice the circumference). - So the torque will be roughly twice that given by the motor. - Less some loss due to friction between the teeth. Establishing gear reduction Teeth provide the active physical connection between the two gears. The force is transferred from one gear to another. Gears are ultimately characterized by the number of teeth. Given, of course, that the teeth are the same size at the interface between two gears. Speed always decreases when going from a smaller gear to a larger gear. And vice versa. Example: Speed reduction from 1000 r/min to 5 r/min. Reduction ratio of 200:1. Impractical to have one gear do this. - One gear with 10 teeth and another with teeth. Lecture 8, Page 3 of 7
Can start with the following arrangement. - There is a larger gear with a smaller gear permanently attached to the shaft. - Called a pinion. - What reduction does this provide? 12 to 60 1/5 12 to 48 ¼ Total: 1/20 - Then reduce even further with a single gear that accomplishes 1/10. - Like a 12 tooth pinion and a 120 tooth gear. - Or use two gears, for example that do 1/5 followed by 1/2. Motors and gear reduction It s always easiest to use DC motors with gear reduction boxes already built into them. Lecture 8, Page 4 of 7
The important specification is the output speed of the gearbox, not the actual running speed of the motor. - And maybe also the output torque of the gearbox, once again not the motor itself. Output shafts can be opposite the input shaft, on the same side as the input shaft, or at 90 degree angles (called a right-angle drive). One can also add reduction boxes, or make them yourself. But there are many pitfalls. - Shaft diameters of motors and gearboxes may be hard to match. - Separate gear reduction boxes are hard to find, but might be cannibalized from salvage motors. - When making your own, meshing gears must exactly match the teeth. - Even small errors can cause the gears to mesh improperly. Lecture 8, Page 5 of 7
There are several types of teeth for gears. Spur gears are the most common, with teeth around the edge of the gear. The of the gear is the number of teeth on a gear divided by the diameter of the gear. - Common pitches are 12, 24, 32, and 48. - Which pitch would have the smallest teeth? 48 teeth per one inch diameter verse 12 teeth per one inch diameter. - Some gears have extra-fine 64-pitch teeth, but only for miniature mechanical systems. Some gears, like worm gears and rack gears hold their position even when the motor is not energized. - Good for arm mechanisms. The pressure angle of the gear is the slope of the face of each tooth. - The most common pressure angle is 20º. - But some use 14.5º. - Meshing two gears with different pressure angles is possible, but some wear will occur. Lecture 8, Page 6 of 7
Belts and chains Akin to the gear are pulleys, belts, sprokets, and chains. Belts with pulleys. Chains with sprokets. They just allow the gears to not need to physically touch. II. Mounting considerations Mounting of a motor may need to be quite precise. And requires careful attention. Connecting the shaft of the motor to a gear, wheel, lever, or other mechanical part is probably the most difficult task of all. Lecture 8, Page 7 of 7