Pressure angle is the angle between the common normal at the cycloid–pin contact and the instantaneous velocity direction at that point. It governs how effectively force turns into torque. Lower in the working region means better load transmission, lower sliding, higher efficiency, lower heat, less wear, and reduced transmission error.
We will be using the Cycloidal Simulator tool to illustrate the implications of pressure angle in the design of a Cycloidal Drive
the eccentric causes the disc’s center to orbit; the disc counter-rotates slightly each input turn (precession), producing the speed reduction.
each engaged lobe pushes on a pin along the common normal; multiple contacts share load simultaneously (higher stiffness, lower stress per contact).
the orientation of that common normal relative to the instantaneous path of the contact point defines the pressure angle, the core metric we’ll use to reason about efficiency, wear, and accuracy.
Pressure angle is the absolute angle between the common normal at the point of contact and the instantaneous velocity direction at that same point.
Mathematically (vector form):
Let’s explore a real example to see how the parameters affect the pressure angle. We will use the Premium version of the Cycloidal Simulator. However, you can still use the free version to follow along.
There are four parameters that play a role in the pressure angle calculation, let’s start with these values (all in mm):
If we input these values into the Cycloidal Simulator, a pressure angle plot is generated for a single pin. The pressure angle is given as a function of the input rotation (eccentric cam rotation) from 0 to 360 degrees (one revolution).
For example, at an input rotation of 240 degrees, the pressure angle will be 60 degrees, this is illustrated in Figure 4. Where the red vector is the common normal, it starts at the pin center and goes through the point of contact between the external pin and the cycloidal disc. The green vector is the instantaneous velocity; it is perpendicular to the dashed green line. Dashed green line goes from the cycloidal disc center and the point of contact with the external pin.
Each pin (in this example we have 30) will have a similar pressure angle curve but with a phase shift. So, we can overlap all curves to create an effective pressure angle for the system. This is shown in Figure 5.
The ring diameter determines the overall size of the cycloidal drive. Typically, we want the drive to be as compact as possible. However, one limiting factor is the transmission ratio that we want to achieve. If the ring diameter is too small, we won’t have enough physical space to fit all external pins, which has a direct effect on the transmission ratio.
In terms of pressure angle, we can see in Figure 8, the incentive is similar, increasing ring diameter increases the average pressure angle, which is undesired. However, Design B does shave a smoother pressure angle variation (given by ‘Pressure Angle Range’) so if lower torque and speed fluctuations is prioritized, then perhaps a larger Ring Diameter will be a better fit for that specific application.
Typically, this parameter is set as this directly determines the transmission ratio. However, if some flexibility is allowed, the rule of thumb is that a larger number of external pins is desired. This allows better distribution of forces.
Pressure angle links directly to efficiency and heat generation. As 𝛼 increases, a larger share of the contact force drives sliding rather than pure rolling, which raises sliding power loss, oil-film shear, and temperature; measured efficiency drops for the same torque and speed. Steep spatial changes in 𝛼 also amplify torque ripple and acoustic noise, especially near reversals.
Manufacturing and assembly tolerances shift both the location and magnitude of the low 𝛼 region. Variations in pin diameter, center distance, and eccentricity can push contact toward the tip or root where is high; a design that is nominally acceptable may run hot or wear quickly in production. Reserve clearance and use profile modification so that, across tolerance extremes, load stays in the intended low segment.
Finally, anti-backlash mechanisms interact with 𝛼. Preload reduces lost motion but biases contact into higher 𝛼 zones during reversals and can increase sliding and heat. Treat preload, surface finish, lubrication, and the modification profile as a set: target the smallest preload that meets backlash requirements while preserving low 𝛼 load transfer and acceptable stress.
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