When doing an animation, I suggest you use the existing Mate dimensions to control part positions.
At time 0 you have all the mates as set up in the assembly.
To have a part move at say 4 seconds, I would Copy the time 0 mate and paste at time 4.
Then move the timeline to when the motion stops (say 10 sec) and paste the same Time 0 mate. Now EDIT that mate and enter the desired new dimension.
Now you will see the part stays still for 4 seconds, then starts moving.
The motion horizontal bar will only appear from 4 sec to 10 sec.
The way you have it set up the motion happens from time 0 to time 14.
Note that doing mates for an animation requires a bit more work than for a static assembly. For example, instead of Coincident mates you need to use Distance = 0 for parts that start touching but will be moving later.
I will set up a new configuration ("Animation") and suppress those existing coincident mates and add new distance mates.
Thank you Bill! Appreciate it and will study further and will try what you have said.