In gear geometry there are 3 main angles, which can be misleading:

  1. Profile angle
  2. Pressure angle
  3. Operating pressure angle

Further for simplicity I would restrict the area of interest to "spur gears". It is quite obvious that for standard mating gears these above mentioned angles are equal, but how do they differ when a profile shift occurs?

We can distinguish 2 types of corrections:

  1. $V_0$ shift $\longrightarrow \sum x = 0$
  2. $V_+ V_-$ shift $\longrightarrow \sum x \neq 0$

So how these angles:

  • are geometrically defined?
  • change during profile shift?
  • can be calculated?
  • 1
    $\begingroup$ Why are they misleading? Which reference book are you using? $\endgroup$
    – Solar Mike
    Nov 26, 2023 at 18:05
  • $\begingroup$ @SolarMike I saw different books and still it is not clear to me. If you feel comfortable in this branch of study please share your answer. $\endgroup$
    – Richard
    Nov 26, 2023 at 19:07

1 Answer 1


In spur gears, the profile angle, pressure angle, and operating pressure angle usually align for standard gears. But with profile shift, things change.

The profile angle, which is the slope of the gear tooth relative to the gear base circle, remains constant even with a profile shift. The pressure angle, the angle at which gear teeth transmit force, and the operating pressure angle, the pressure angle during gear operation, are the ones affected by profile shift.

In a V0 shift (∑x=0), the gears are modified but the center distance remains the same, whereas in a V+V− shift (∑x≠0), the center distance changes. These shifts alter the effective working pressure angle: a positive shift increases it, and a negative shift decreases it.

Calculating these angles post-shift involves gear tooth geometry and the involute function. It's complex and often handled by specialized gear design software, but can be done manually through detailed geometric analysis if necessary.


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