ENGR 107 – Introduction to Engineering Simple Machines and Mechanical Advantage (Lecture #4) ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Simple Machines ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Simple Machines A mechanical device that changes the magnitude or direction of a force. ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Simple Machines The six classical simple machines are: Lever Wheel and axis Pulley Inclined plane Wedge Screw All complex machines are constructed from one or more of these simple machines. ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Simple Machines Simple machines can be classified as follows: Those dependent on the vector resolution of forces Inclined plane Wedge Screw Those in which there is an equilibrium of torques Lever Pulley Wheel ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Lever ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Wheel and Axle ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Pulley ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Inclined Plane ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Wedge ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Screw ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Simple Machines A simple machine uses an applied force to do work against a load. Work done on the load is equal to the work done by the applied force. Can be used to increase the force acting on the load, at the expense of a proportional decrease in the distance that the load is moved. The ratio of the force acting on the load to the force applied to the simple machine is known as the mechanical advantage. ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Mechanical Advantage ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Mechanical Advantage The factor by which a simple machine multiplies the force or torque applied to it. ENGR 107 - Introduction to Engineering

MA = output force / input force Mechanical Advantage MA = output force / input force applied force force acting on load ENGR 107 - Introduction to Engineering

MA = distanceapplied force / distanceload moved Mechanical Advantage MA = distanceapplied force / distanceload moved ENGR 107 - Introduction to Engineering

Mechanical Advantage WorkIN = WorkOUT Force applied x distanceapplied force = Force acting on load x distanceload moved ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Lever ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Pulley ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Pulley r1 r2 input output ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Torque (Moment) The tendency of a force to rotate an object about an axis, fulcrum or pivot. ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Torque (Moment) ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Torque T = F x d d = Distance measured from the point of rotation to the applied force F = applied force perpendicular to the measured distance ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Mechanical Advantage MA = T2 / T1 = r2 / r1 output input output input T = torque r = radius ENGR 107 - Introduction to Engineering

T2 = MA x T1 F2 x d2 = MA x (F1 x d1) F2 = MA x F1 x (d1 / d2) Mechanical Advantage T2 = MA x T1 F2 x d2 = MA x (F1 x d1) F2 = MA x F1 x (d1 / d2) ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Gears ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Gears ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Gears Gears may be considered a simple machine. Two or more gears working in tandem can produce a mechanical advantage. Gear ratio Unequal number of teeth Gears in a transmission are analogous to wheels in a pulley. ENGR 107 - Introduction to Engineering

MA = T2 / T1 = #Teeth2 / #Teeth1 Mechanical Advantage MA = T2 / T1 = #Teeth2 / #Teeth1 output input output input T = torque #Teeth = # of teeth on gear ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Velocity Reduction ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Velocity Reduction VR = 1 / MA ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Velocity Reduction VR = T1 / T2 = r1 / r2 input output T = torque r = radius ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Pulley r1 r2 input output ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Gears r1 r2 input output ENGR 107 - Introduction to Engineering

Angular Speed A measure of the speed of rotation about an axis. Often specified in revolutions per minute (rpm). ENGR 107 - Introduction to Engineering

ENGR 107 - Introduction to Engineering Angular Speed w2 = VR x w1 output input w1 = angular speed of input wheel or gear w2 = angular speed of output wheel or gear ENGR 107 - Introduction to Engineering