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Gears, Pulley Drives, and Sprockets Gears, Pulleys, & Sprockets Mechanisms used to transfer energy through rotary motion. Change the speed of rotation Change the direction of rotation Change the amount of torque available to do work Gears A gear train is a mechanism used for transmitting rotary motion and torque through interlocking teeth. A gear train is made when two or more gears are meshed Driver gear causes motion Motion is transferred to the driven gear Gears Mating gears always turn in opposite directions. An Idler Gear allows the driver and driven gears to rotate in the same direction. Mating gears always have the same size teeth (diametric pitch). Gears The rpm of the larger gear is always slower than the rpm of the smaller gear. Gears locked together on the same shaft will always turn in the same direction and at the same rpm. Gear Ratios Variables to know n = number of teeth d = diameter ω = angular velocity (speed) τ = torque 4” ** Subscripts in and out are used to distinguish between gears ** nin= 6 nout = 12 din = 2in. dout = 4in. ωin = 40rpm ωout = 20rpm τin = 40 ft-lb τout = 80 ft-lb Gear Ratios Equations to know GR = Gear Ratio GR = MA nout dout GR 1 nin din ? 1 2 1 12 6 4in. 2in. in out 40rpm 20rpm out in 80 ft lb 40 ft lb Gear Ratios What is the gear ratio between gear A and B? nout GR 1 nin What is the gear ratio between gear B and C? 5 .42 nout GR 12 1 1 nin What is the gear ratio between gear C and D? 20 4 nout GR 5 1 1 nin 12 .6 20 1 Gear Ratios What is the TOTAL gear train gear ratio? 0.6 0.42 4 1 1 1 1 1 If gear A and D are directly nout 20 1 GR connected to each other what 20 1 1 nin would the resulting gear ratio be? What would the Total gear ratio be if the last gear had 40 teeth? nout GR 40 2 0.6 0.42 8 2 or 1 nin 20 1 1 1 1 1 Compound Gear Train Driver The two middle gears share a common axle, so they rotate at the same speed. This allows the final gear to rotate slower and produce more torque than if it were connected only to driver gear. Compound Gear Ratios D B A C 20 T 10 T 40 T 50 T What is the gear ratio between gear C and D? GR nout 1 nin What is the gear ratio between gear A and B? GR nout 1 nin 40 4 10 1 50 2.5 20 1 What is the gear ratio of the entire gear train? 4 2.5 10 1 1 1 Equations out in 2in. Pulley and Belt Systems dout in out din out in 6in. 2in. d = diameter 30rpm 10rpm 55 ft lb 1 18 ft lb 3 ω = angular velocity (speed) τ = torque Sprocket and Chain Systems 3in. 1.5in. in out nout dout out in nin din out in 22 11 n = number of teeth 3in. 1.5in. d = diameter 90rpm 120 ft lb 45rpm 60 ft lb ω = angular velocity (speed) τ = torque Comparing Pulleys and Sprockets Pulley Sprocket Method of Transmitting Force Belt Chain Advantages Quiet, no lubrication needed, inexpensive No slip, greater strength Higher cost, needs lubrication, noisy Disadvantages Can slip Image Resources Microsoft, Inc. (2008). Clip Art. Retrieved January 15, 2008, from http://office.microsoft.com/en-us/clipart/default.aspx