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Inclined Plane, Wedge, and Screw The Six Simple Machines Mechanisms that manipulate force and distance. Lever Wheel and Axle Pulley Inclined Plane Wedge Screw A flat surface set at an angle or incline with no moving parts Able to lift objects by pushing or pulling the load FR AMA = FE 4 ft What is the AMA of the inclined plane above? 50.lb AMA = 20.lb AMA = 2.5 = 2.5:1 What is the efficiency of the inclined plane above? 2.50 AMA = 0.67 or 67% Efficiency = 3.75 IMA • Functions as a moving inclined plane • Tapers to a thin edge • Used for splitting, raising heavy items, or tightening by expansion (being driven into something) DE = Distance traveled by the effort = L 10.0 in. L DE IMA = DR H 3.0 in. DR = Distance traveled by the resistance = H L IMA = H What is the IMA of the wedge on the right? IMA = 10.0 in. / 3.0 in. = 3.33 = 3.3:1 250. lb What is the AMA of the wedge on the right? 700.lb AMA = 250.lb L 10.0 in. FR AMA = FE H 3.0 in. AMA = 2.80 = 2.80:1 What is the efficiency of the wedge on the right? AMA 2.800 = 0.84 or 84% Efficiency = 3.333 IMA Two Components: • An inclined plane wrapped around a cylinder, forming the screw’s “pitch” • A wheel and axle used to create rotary motion Properties: • • • • Change rotary motion into linear motion Used as a threaded fastener Large amount of friction loss (is this good or bad?) Large MA Effort Arm Distance If using a wrench, effort arm distance would be the length of the wrench Pitch Distance between threads, also the linear distance traveled in one rotation of the screw. Example: a screw has 13 threads per inch, 13 TPI for short. The pitch (distance between threads) is 1/13 of an inch. Q: How far will a screw with 13 threads per inch advance if turned one full rotation? A: 1/13 of a inch Diameter Standard Thread Information 1/4 x 20 x 3.0 NC Pitch Length in (TPI) Outside inches diameter of (Optional) screw shaft (inches) Thread description coarse or fine (Optional) Metric Thread Information M3 x 0.5 x 30 M = Metric Outside Pitch diameter of (mm per screw shaft thread) (mm) Length in mm (Optional) Unified Thread Information #4 x 40 x 2.0 NC Pitch Length in (TPI) Outside inches diameter of (Optional) screw shaft (inches) Thread description coarse or fine (Optional) • In Unified threads (measured in inches) there are numbered diameters #0 through #10 • #0 the smallest and #10 is the largest • The major diameter in Unified Threads = 0.060" + 0.013" X (numbered diameter) • Example: A #2 has a major diameter of 0.086" DE IMA = DR 1/4 20 NC DE = One rotation of the effort = Circumference DR = Linear distance traveled during one rotation = Pitch Circumference 2πrE IMA = = Pitch P What is the IMA of the screw above if effort is applied by an 8.0in. long wrench? 2π8.0in IMA = = 1005.31 = 1.0 •103 1in 20 FR AMA = FE 1/4 20 NC 35 lb What is the AMA of the screw? 1200lb AMA = 35lb AMA = 34.29 = 34:1 1200 lb What is the efficiency of the screw? AMA Efficiency = IMA 34.29 = 0.0341 or 3.4% 1005.3 Why is efficiency so low? Simple machines working in combination to complete a task Calculating mechanical advantage MA = MA1 MA2 MA... Microsoft, Inc. (2008). Clip Art. Retrieved January 10, 2008, from http://office.microsoft.com/en-us/clipart/default.aspx