The purpose of mechanism is transmit motion and force (or torque) from one location in a flight vehicle to another. The challenge when designing a good mechanism deals with the relationship between position and force (which always hold and becomes a constraint on the design) and the fact the equations are inherently nonlinear (although a mechanism can be approximately linear over a short travel). The relationship between position and force is through the mechanical advantage relationships.
Kinematic analysis deals with position and velocity analysis. However, the mechanical advantage in a mechanism is usually of design importance. Using kinematic velocity analysis a relationship between kinematics and force/torque transfer can be developed.
The fundamental work and power relationships are
Work = F * d
Power = F * d / t = F * Vel
If the input to the mechanism is a force, Fin, with a velocity component, Vin, then
Pin = Fin * Vin
or for a torque input,
Pin = Tin * ωin
Likewise, for power out
Pout = Fout * Vout
or for a torque output,
Pout = Tout * ωout
Note that an input force or torque can produce either an output force or an output torque.
Therefore, since Pin = Pout (ideally), the mechanical advantage (MA) can be written as
or
These relationships are dimensionless.
For cases where an input force produces an output torque (or vice versa)
or
In English units, these dimensions are rad/sec to ft/sec and lbs / lb-in (or the inverse).
Therefore, a power or force or torque requirement can be converted to a velocity ratio, and velocity analysis can be used to design a mechanism for a required mechanical advantage. However, keep in mind that velocity ratio is normally a function of mechanism position and hence mechanical advantage will be function of mechanism position.
From a mechanism design process, when given a mechanical advantage requirement, convert this relationship to a velocity ratio and use kinematic analysis to design the mechanism. Kinematic design approaches are discussed in the gear and 4 bar linkage modules.