So arcs aren't always good.
Heres an example of an arrow hitting a target, and an arrow missing the target.
One more example with a rigged character.
One more example with a rigged character.
All I have done is set a key at 1 and 25 the same. set a key on 13 the opposite. set a key on 7 and 19 the opposite again and splined it. And you pretty much get a perfect circle. So if you are blocking in a hand doing a circle arc you know how its done. frame one = 5y frame 25= 5 y frame 13 = 5y. frame 7 = -5x frame 19 = +5x and just spline it up. This is what you get.
Figure 8 now.
same formula as before pretty much. Just a couple more keys in the y axis and you have a figure 8.
well pose 2 wasn't indicated in the book but it's my breakdown pose. So it gives a few examples of how to animate this so here are the clips.
This first one the breakdown pose was at frame 4 the final pose frame 5.
This second one the breakdown was at frame 2 with the point on frame 5
This third one the break down was in the middle, and I slowed in and out of the pose
This one I just decided to have some fun and make something a little snappy.

Yet this is what we will get when animating ik, is the image on the upper right. Yet ik seems to be how most of are animating lately. Why do we get this when animating in ik? Well ik deals only in terms of translations. So the computer plots out the fastest way to get from a to b, and we get this straight path of action, with no arc whatsoever. The movement is completely unnatural. If we were to animate in fk, we wouldnt have to worry so much about our arcs, as the computer would rotate from a particular pivot point and the arcs would create the obviously more natural movement. So i'm going to create the pendulum and animate on in ik, and one in fk with just a basic sphere. So I went and animated the resulting pendulum based on the diagram given, in fk.
So its going pretty good. Im not a fan of the timing, but its the diagram given :S
Now I've done one the exact same timing in ik and heres what we get.
Well,its not really working is it. I guess I have to go in and work some more. I only need to animate the one axis in fk, but in Ik I need to go in there and do some more work. Guess I better go do it.
Same result, just more work.
editor so I have a little trick ive made up. I open both the y and x axis scaling curves. I add a breakdown key with both curves selected(I on the keyboard and mmb click) and I turn my scale tool on(r) and grab both breakdown keys at the same time. I click on the 1 line and can now scale them both to where I want the breakdown to be and they move exactly the same so the breakdown volume still = 3 and the journey to it will always = 3 as well. Here is an image of how that looks.
And one with ease in and ease out, or slow in and slow out. He gives somewhat of an example of a timing chart as well. Which i'll explain how I go about animating the coin to the provided timing chart. On the chart you will notice on frame 13 which is exactly the middle, the coin to is exactly at the middle. Frame 11 is at 50 percent of the distance to frame 13 and frame 15 is at 50 percent of the distance to the final frame. Likewise frame 9 and 17 are 50 percent away as well. 

You can now smooth out your curves and your animation for this will look exactly as the example given. Which is like this.
d press "s" to do this, I move over to frame 60 I move my ball to the opposite side of the screen and press "s" again. I know because my timing has been worked out I need 59 frames to get from point a to point b. So now when I press play I can see my ball travelling to this point, but theres no bounce. I want to change how it is getting there though so I open my "graph editor". This is under window, animation editors, graph editor. So with the ball clicked I can see a line there that represents the travel path. I drag my mouse over the line and change my curves to linear so the ball moves evenly spaced on this path. I go into the time slider and press "s" on frame 20 36 49 and 59. This exactly where I want the ball to be on these frames.
Now I need to animate the bounce. So I go to frame 10 and translate the ball up in "y" axis to where I want the ball to peak on the bounce. I do this for all the 4 bounces I do, remembering the ball wont bounce as high on the following bounce. This is looking pretty ugly but its bouncing. So I need to work on my spacing now. I drag my mouse over the y curves and click the spline button, which flattens all the curves. I now need a key inbetween each key that will control the spacing, or control how the ball will get from the bottom to the top, and the top to the bottom. So I hold "i" on the keyboard and middle mouse click between each point to add the keys I need to control the spacing.
. Up and down would change the height of the key , and side to side would change the frame the ball will contact that height. You can see how my curves end up looking after I have adjusted the "inbetween" keys. Also notice I the bottom tangents are red and blue. This means I have broken them. This allows me to grab one half of the tangent and pull it around without affecting the other half. Which is really helpful for a bounce like this. To move the tangent around, just select the side of it you want to move, and middle mouse click and move it around to where you want it to be.