This topic:
•  Reviews Payload Types. 
•  How we can normalize Payload Types with coefficients: Q, K, Cm 
•  Reviews the effect on inputtorque from different payloads types, and how we can normalize it as the coefficient, Cc 
Notes on the Terms: Payload, Duty and Capacity.
The 'payload', also named 'load', is the total force, or torque, referred to the camfollower.
The 'load' imposed on a cammechanism is also known as the duty of the mechanism.
The capacity is the ability of the mechanism to perform the duty for a specified lifetime.
It is important to know the payloadtype, or loadtype, when we design a cammechanism. The outputload is passed from the camfollower and back to the cam and the camshaft. Thus, the inputload that is imposed on a camshaft is a function of the loadtype at the camfollower. The different loadtypes result in different loads on the camshaft. The nominal output loading, which will be a Force for linear motion, and a Torque for rotary motion, is derived from the following 'PayloadTypes'. 

A: Force or Torque: constant. For example, friction, gravity, work loads. 

B: Force or Torque: proportional to displacement. For example, a spring. 

C: Force or Torque: proportional to velocity. For example, viscosity. 

D: Force or Torque: proportional to acceleration. For example, inertia. 

E: Force or Torque: conforms to a special function. For example, an engine cycle. 

EXAMPLE 1A: Gravity, Spring and Inertia: Speed Dependence 

MECHANISM AT 'LOWSPEED' 
The two images to the left show the same load types on a cam mechanism, at two different speeds. The Payloadtypes are:
You can see that at 'highspeed' the inertia is greater. At the higher speed the load becomes negative at point, along the deceleration of the rise. 

SAME MECHANISM AT 'HIGHSPEED' 

Example 1B : Gravity, Spring and Inertia: Different Preload of SpringThe image below shows the period of negative loading when the cam has a 'falling' motion. In such a case, the camfollower would lose contact with an open track cam and control of the payload would be lost. To make sure the camfollower remains in contact with the camprofile:
 or 


Virtually all indexing mechanisms, and many reciprocating and oscillating mechanisms, have a duty that combines a Constant (A) and an Acceleration (D) load, with less significant amounts from the other kinds of loads. Constant Load  from friction forces (bearing seals), raising weights or gravitational force, and other work loads  can be resolved into a single force or torque resisting the output motion. Acceleration Load  from the inertia of various masses  can be resolved into a single equivalent inertia connected to the output or the camfollower. Total load = inertia load + constant load. The peak of the total load usually is at the same point as the maximum inertia load. 

Other common Payload Types
See example above  same mechanism at two different machine speeds.
The maximum value and proportion of each load type component (A, B, C, D and E), depends on the application. Thus, there is an infinite number of load patterns. It is possible to tabulate normalized values for the most common combinations. Payload for Conjugate CamsThe idealised design of Conjugate Cams eliminates the need for a Spring to maintain the contact of the roller against the cam. Frequently, the camfollower rollers are adjusted, or designed, to give an 'optimal' preload against the cam, so that the rollers do not slip. This is an 'idealised design'. More frequently, manufacturing and machining tolerances, mean it is difficult to guarantee contact between the cam and the roller throughout the cam's rotation. The roller will often lose contact during some part of the machine cycle. Frequently, Conjugate Cams use a spring, aircylinder or hydraulic device, to force one of the camfollower rollers against the cam to eliminate backlash. The loading device only needs a short travel to compensate for manufacturing tolerances. 
Inertia LoadThe maximum inertia load is: [Using these simple equations: F= M.a ; T=I.α 

and


The Inertia Load Coefficients Fi or Mi are 'nominal', and must be modified by the application of the TorsionFactor, Ct. Friction LoadThe constant load, such as friction, is:
Referred to the mechanism output in both cases. Add the Friction Load to the Inertia Load. Spring LoadWhen there is an output force component that is proportional to displacement, such as a spring force, it is convenient to add the maximum value spring force to the FrictionForce, Ff , or FrictionMoment, Mf as if it were a constant load. In that case, the total outputload calculation is conservative. You can take these as safe values for preliminary designs. Load Mix: Inertia; Friction; SpringInstead of adding the 'Maximum SpringRate Force' to the 'Constant Load', we can take all three load patterns into account. When appropriate, the total maximum load can be adjusted downwards by a loadmix coefficient, Cm. Thus: Cm depends on the relative values of constant load to spring load and also inertia load. 
Preload Coefficient, K
Inertia Ratio, Q

The input torque [drive torque] varies throughout the motion. The variation is a function of the output load pattern and the motionlaw. Since the output load pattern varies with the mix of inertia load, spring load, and constant load, so too does the input torque. For all cases, the mix is defined with the factors Q and K , as defined above. For each motionlaw, the instantaneous input torque can be expressed as a function of the instantaneous output load: 

for linear motion 

for rotary motion 

Where: : 

The instantaneous output load, fo or mo, is a function of the normalized motionlaw factors, the load mix, and the payload. Thus, the above equations can also be expressed as: 

 or  The maximum value of occurs during the acceleration phase. It can be simply expressed by introducing a normalized InputTorque Coefficient, Cc. Input Torque Coefficient (No Spring Loading, K =1)Thus: 

for linear motion 

for a rotary motion. 

Mc 
= Peak Input Torque 

Cc = the maximum of: 


The value of Cc, the Input Torque Coefficient, can be evaluated for any motionlaw and a range of load mix factors. The input torque patterns for some standard motionlaws are shown (below) for different values of Q and when K=1 [no spring loading]. From these patterns it can be seen that there is a wide disparity between the input torques of different motionlaws, for all values of Q. 

Input Torque Coefficient, Cc [K= 1, and Q= 0 – 1] 

Drive Torque Fluctuations with each MotionLaw. It is common to use the maximum value of the Input Torque Coefficient, Cc, when the inertia ratio, Q=1
However, if this motionlaw is preceded or followed by a dwell, then there will be a discontinuity of acceleration at the start and end of the motion, and the dynamic response may be unacceptable. 

It can cause severe overrun if the input transmission has low inertia and low rigidity. 



This makes the ModSine very tolerant of a bad input transmission which, combined with its good dynamic response properties, is the reason for its popularity. 

This image shows the: Peak Values of InputTorque Coefficient Cc against Q , Inertia Ratio, for each motionlaw for constant loading (K=1). 

Input Torque Coefficient, Cc [K= 0–1 & Q = 0–1]The more complex loading pattern that includes a spring load component (0<K<1) we can find that both peak output load represented by Cm and the peak input torque, represented by Cc, are considerably reduced with low preload ratios. 
