Animating a rotation but with acceleration

Question

I am working on an animation where a wheel is rotating. This has been done using the 'cycles' modifier on an F-Curve. Now I want it to slowly start up a few seconds into the video, and from frame X on, it should rotate at constant speed.

Adding the accelerating animation is quite simply done by inserting a keyframe before the rotation and adjusting the graph accordingly. However, the cycles modifier insists on repeating the acceleration part of the curve, too. In my case, I need the modifier to only repeat the constant rotation. I have not found a way to restrict the keyframes that should be repeated with the 'restrict frame range' settings. Can this be done and I just haven't seen it?

After inserting acceleration:

Expected graph (edited):

Answer 1

Unfortunately, the cycles modifier can't be set to repeat only a certain part of the action. You have two alternatives.

Linear Extrapolation

Press Shift+E and choose Linear Extrapolation. This way the wheel will keep rotating based on the last two keyframes up to infinity.

Use Non Linear Animation

Go to the NLA editor. Press the down button. The active action will be converted to an action strip. I have duplicated the action strip with Shift+D and moved it to the frame, where the original strip ends.

With the second strip selected, we can set it to the original action, if a duplicate action was made, although this is not necessary.
Set the Start Frame to your second keyframe, frame which one one the wheels rotation has reached its final speed. Set the End Frame to the last keyframe. Set the repeat scale as desired.

This way the linear motion of the action is isolated and repeated.