Simple Machine
Simple Machines Changes effort, displacement or direction and magnitude of a load 6 simple machines Lever Incline plane Wedge Screw Pulley Wheel and Axle Mechanical Advantage Ideal: IMA = Actual: AMA= Effort Distance = Load = L Load Distance Ideal Effort E I Load = L Actual Effort E A Efficiency how the effort is used to move the load Losses due to friction or other irreversible actions η= Energy used Energy supplied =AMA IMA = E I E A Note: (Effort Distance Effort) =(Load Distance Load) or E in =E out Note: (E A =E I -Loss) 2/25/2016 MCVTS CMET 2
Lever Levers magnify effort or displacement Three classes of levers based on location of the fulcrum Class 1 lever: Fulcrum between the Load and Effort Examples: See-Saw, Pry Bar, Balance Scale Class 2 lever: Load between the Effort and Fulcrum Examples: Wheelbarrow, Nut Cracker Class 3 Lever: Effort between Load and Fulcrum Examples: Elbow, Tweezers IMA Lever = d E d L = L E I AMA Lever = L E A η= AMA Lever IMA Lever = E A E I Effort 150lb η=0.9 IMA = d e = 8 d L 4 = 2 E I = L IMA = 150 2 = 75lb AMA = ηima = 0.9 2 = 1.8 E A = L AMA = 150 1.8 = 83.33lb 2/25/2016 MCVTS CMET 3
Incline Plane Decreases effort to move a load to a new height or vertical rise Friction opposes motion up the ramp increasing the effort required IMA = s h = 1 η= sinθ Energy used Energy supplied =AMA = E I IMA E A Ex. An incline plane with 20 slope is used to move a 50-lb load a vertical distance of 36 inches. The actual amount of effort force that is needed to move the load up the inclined surface is 25lb. Find: a) Travel distance b) Ideal mechanical advantage c) Actual mechanical advantage d) Efficiency, η e) Ideal effort Vert. Rise (h) θ w a) s = h = 36 = 105.3 in sinθ sin20 b) IMA = s = 105.3 = 2.92 h 36 c) AMA = L E A = 50 25 = 2 d) η = AMA IMA = 2 2.92 = 0.68 e) E I = L AMA = 50 2.92 = 17.12 lb θ 2/25/2016 MCVTS CMET 4
Wedge Wedge is similar to incline ramp but different things move Incline Plane o Incline plane is stationary o Only one surface is involved Wedge o Wedge moves and load is stationary o Friction forces on both sides of the wedge Wedge benefits Redirects force from horizontal to vertical or vice versa Uses friction forces to create self-locking designs Usese: Splitting wood, Door stops, Shimming to level items, raise or lower objects, etc. Wedge Force P moves wedge if it overcomes friction forces Sliding occurs on three surfaces and subjected to friction forces Two conditions with applied force o Does it overcome the friction force? o Does the downward force of the weight, W, overcome the friction force and the applied force, P, if any, so that the wedge pops out. 2/25/2016 MCVTS CMET 5
Wedge Free Body Friction force opposes motion Applied force to the right controls movement of the weight Wedge weight is considered negligible as compared to the load weigh Raising Weight Lowering Weight Non Self-locking Lowering weight Self-Locking 2/25/2016 MCVTS CMET 6
Friction force - Revisited Friction force opposes motion Friction force is proportional to the normal force F f =μ s F N where μ s is the coefficient of static friction and F N is the normal force Friction force, F f can also be expressed as a Friction Angle, ψ o tan ψ = F f F N, where R = F N 2 + F f 2 ψ F F F N 2/25/2016 MCVTS CMET 7
Example Block A supports a load W=100kN and is to be raised by forcing the wedge B under it. The angle of friction for all services in contact is f=15. If the wedge has a weight of 40kN, find the value of P : a) To start the wedge under the block b) To pull the wedge out from under the block 2/25/2016 MCVTS CMET 8
Solution 2/25/2016 MCVTS CMET 9
Problem Part 2 2/25/2016 MCVTS CMET 10
2/25/2016 MCVTS CMET 11
Wheel and Axle New Uses the mechanical advantage to either magnify the applied force or magnify the motion Raising Bucket: Load is inner shaft Effort on large wheel d 1 d 2 Driving Car: Load is tire Effort is drive Axle F 1 F 2 Mechanical Advantage: MA Ideal = Load Effort = Effort Dist. Load Dist. = 2π(r 2) 2π(r 1) = r 2 r 1 Efficiency: η= MA actual MA ideal
Basic Screw Terminology Pitch Distance between adjacent threads Lead Distance screw (or nut) advances per full turn Lead=Pitch*Starts (for single thread start=1) Start Number of separate (non-intersecting) threads wound around the same core Maj. Diam. Diameter over the top of the thread Min. Diam. Diameter at the root of the thread Pitch Diam. Diameter through the thread at the point where the thread thickness is equal to ½ the pitch New Standard Thread Designation UNC and UNF XXX-YYY XXX Major diameter For Ø>¼ actual diameter For Ø<¼ Gauge number (4, 6, 8, 10 or 12) YYY- Threads/inch SI Thread Maaa-bbb aaa Major diameter (mm) bbb Pitch (mm/thread) Mechanical Advantage: MA Ideal = Load Effort Efficiency: η= MA actual MA ideal = Effort Dist. Load Dist. = 2π(r effort) lead
Power Screws New Power Screws Used to transmit power or motion Axial movement of nut supplies motion Screw Profiles Square Thread o Most efficient for transferring torque to linear motion Acme Thread o Easeier to make o Good when well lubricated o Efficeincy slightly lower than Squrare thread Butress Thread o More efficient than Acme o Closer to square thread o Used when force is transmitted in one direction only