Thanks much Fredo6. But please don't make this change for shapes only for me. It's a lot of work for just one person and I'm sure you have lots of other work to do. If there are other people who would benefit from this perhaps they can mention this in this message thread.

The ability to control starting and ending speeds provides the ability to select whatever constant acceleration is desired. Great! Thanks very much Fredo6. However, as I wrote in a previous post, I have realized that I need a parallel ability to control acceleration in shape change motions along an axis. I imagine that I am the only person who needs such a feature. So I doubt it would be worthwhile to add this to Animator.

Thanks Fredo6. My understanding is that easing does produce acceleration during particular intervals within a segment since velocity changes during those intervals. But easing does not produce average acceleration for a segment as a whole since average velocity doesn't change for the segment. This is because velocity is fixed by the time and distance for the segment. Therefore any acceleration that occurs in particular intervals of a segment is balanced by deceleration in other intervals. But easing does produce acceleration in the sense the velocity is different at the start than at the end of the segment. However its better for my purposes to be able to control acceleration for a segment by editing the displacement vs. time curve for the segment. Though I doubt that many other users would want this capability.
Thanks much for your help.

derei: As you described, easing is applied to a segment without changing the average velocity for the segment as a whole. The same would be true for non-zero starting velocities.

derei: Currently in Animator it's not possible to specify starting and ending velocities for translations. The velocity of a segment is determined by its distance and time, as you mentioned, or by entering the velocity directly. However translations begin at zero velocity. Fredo6 wrote above that in a new version available Monday it will be possible to specify starting and ending velocities for translations and rotations. However, I also need to specify starting velocity for shape change motions along the axis along which the shape change occurs. I'm not sure if Fredo6 will provide this option also.

To clarify, I need to be able to give scaling movement a starting velocity rather than have it starting stationary.

One more question, Fredo6...

I need to apply the same acceleration and deceleration to object scaling. Is that possible? Or can I accomplish this using a kinematic constraint between a translation element (with acceleration or deceleration) and a scaling element?

Thanks for your help.

Great! Thanks.

No problem Schuppe

If I had a streamlined way to do one translation I could do the rest.
But also didn't mention that I also need to be able to control acceleration for scaling as part of this project. If I can solve the problem for translation then maybe I can use a kinematic constraint to tie acceleration for scaling to translation acceleration. That would work. I don't know if Animator can constrain a scaling movement to a translation movement.
But so far I don't see a practical solution for the translation acceleration problem to begin with.

Is it possible that SketchUp and Animator aren't suited to my application? If no solution emerges I guess I have to try another app. I do like Animator and I've started to get accustomed to using it. My needs aren't super complex but I do need to be able to control acceleration. No complex modeling needed. I'm thinking of trying Blender. It's free and I think it can handle what I need. But it's got a considerable learning curve. I wonder if anyone has other suggestions. I'd even consider 2D though I'd prefer 3D. Maybe Flash?

Thanks for setting up this example, Fredo6. My problem is that I need the object (the green cube in your example) to already be in constant motion at the start. I then want to accelerate this motion. So if the cube is moving at 1 m/s for a while I then want to accelerate it smoothly up to 5 m/s, In your example when easing is applies to the green cube it starts motionless.

I set up a trial in which a cube is first moving at constant speed in translation #1. I then created 4 m ore translations, each at higher speed. I tried two things:

1. I grouped the 4 translations together and then applied easing. The cube moved at constant speed in translation #1. But then it stopped first before it began to accelerate in the 4 grouped and eased translations.
2. I then tried not grouping the translations (as I think Schuppe is suggesting). I got constant motion in translation #1 followed by acceleration in translations #2-#5 as I wanted. But the motion was jerky. I could solve this by creating a large number of translations, each with a small increase in speed. With a large enough number of translations I think I’d get smooth acceleration. But that’s a lot of work considering that I have 12 separate motions I need to do this with. So if each needs 60 or 70 separate elements to end up smooth, that’s 12x 60 or 12x70 elements to create. I can do this if necessary but I’m hoping for an less time-consuming solution.