Mechanisms - Formulae Flashcards
Force
F = ma Force = mass x acceleration
Moment of the force
M = Fd
Moment of the force = force applied x distance from pivot (in metres)
Size of moments in equilibrium
Sum of anti-clockwise moments = sum of clockwise moments
Torque
T = rF Torque vector (magnitude of torque) = position vector (in metres) x force vector
T = rFsin(θ) Torque vector (magnitude of torque) = position vector (in metres) x force vector x angle between force vector & lever harm vector
Mechanical Advantage (levers)
Mechanical advantage (Ma) = load/effort (both in newtons
Mechanical advantage (Ma)= input arm distance/output arm distance
Velocity ratio (levers)
Velocity ratio (VR) = distance moved by effort/distance moved by load
Efficiency
Efficiency = mechanical advantage/velocity ratio x 100%
Mechanical advantage (for pulleys)
Mechanical advantage = load/effect
Velocity ratio (stepped pulleys)
Velocity ratio = driver pulley revolutions/driven pulley revolutions
Velocity ratio = distance moved by driven pulley/distance moved by driver pulley
Output speed (stepped pulleys)
Output speed = input speed/velocity ratio
Velocity ratio (pulleys and belt drives)
Velocity ratio = distance moved by effort/distance moved by load
Gear ratio
Gear ratio = number of teeth on driven gear/number of teeth on driver gear
Output speed (gears)
Output speed = input speed/gear ratio
Mechanical advantage (Weston differential pulleys)
Mechanical advantage = 2R/R-r
R = large pulley radius
r = small pulley radius
Output speed (pulleys)
OS = IS/VR
Output speed = input speed/velocity ratio
