# Rigidty: Transmission Design Considerations

## Transmission Design Considerations of Cam Mechanisms

Input Transmission: all of the transmission components from the power source (usually an electric motor) to the element moving the cam - most often a cam-shaft.

Output Transmission: all of the transmission components from the cam-follower (usually a roller) to the payload  - also called: end-effector, or tool.

The components in the transmissions typically include shafts, gears, gearboxes, couplings, chain drives, belt drives, linkages.

### Three(3) Mechanical Properties of the Transmission:

 The performance, and the ability of the input-transmission and output-transmissions to deliver a motion, is a function of three parameters: Strength... the ability to withstand the forces and torques without fracture or yield. The design must be strong enough to transfer the peak force or torque. The design of components is more in the field of strength of materials, not cam systems. Rigidity... the ability to transmit the force and torque without too much deflection. Rigidity is important in the generation of vibration. All transmission components have elasticity, the reciprocal of rigidity. When a metal component is stressed within its elastic limit, it strains elastically. Its distortion, or deflection, is related to its size and shape, and is proportional to the load applied. When it is stressed beyond its elastic limit it suffers plastic deformation. Plastic deformation does not recover when you remove the stress. It may also suffer hysteresis within the elastic limit. Hysteresis is an energy absorbing phenomenon, whereby the strain produced by an increasing load is not fully reduced by a decreasing load. Hysteresis is responsible for internal damping of vibrations. But this effect is unlikely to be significant in cam systems. To simplify analysis, we assume that transmission components are perfectly elastic with no hysteresis. If there are several components connected in series, as is a typical cam transmission, the deflections add together so that the overall deflection from one end of the transmission to the other is the sum of the individual deflections. When gearing is involved, different parts of the transmission may be subject to different torques and the deflections at one side of a gear pair may be transformed to a different deflection at the other side of the gear. To assess the rigidity of a transmission as whole, therefore, it is necessary to estimate the rigidity of each component and combine them in a particular way. Backlash... lost transmission with a reversal of torque or force. We will review the detrimental effects of backlash in the next topic.

### Input-Transmission: Rigidity and Stiffness

The Input-Transmission includes the power transmission components from the power source (usually a motor) to the cam.

Most cams in industrial machines rotate and they are driven by rotating motors. Thus, the components are rotary, and they will have an angular deflection that is proportional to the applied torque (pulleys and sprockets of belts and chains are also 'rotary components'). The simplest components are shafts, but these are often constructed with sections of different diameters. Shafts that are connected in series frequently have different diameters.

### Output Transmission

The estimation of rigidity of an output transmission is exactly the same as for an input transmission. Most inputs, of course, drive rotary cams and therefore rigidity is expressed as the overall torsional rigidity. With output transmissions, however, we are dealing with a payload that is driven by the cam follower and the motion may be linear (reciprocating) or rotary (oscillating or indexing).

If the follower motion is a translating, linear motion, then the overall rigidity of the output transmission is expressed as a linear stiffness referred to the follower.

If the follower motion is a swinging, rotating motion, then the overall rigidity of the output transmission is expressed as a torsional rigidity referred to the follower axis.