Is there a way to make a figure's hand move under the control of an animated object like a hand crank? Also follow the body part of another figure such as holding hands while walking?

There is a "point at" feature which could help you with your first question. As for the holding hands, a combination of IK and parenting might solve that issue. Maybe someone else who has actually done such animations could guide you the right direction.

What you want to do is add a simple prop such as a box. With IK for the Hand turned on constrain the hand to the box. There will be a new dial created for the constraint, when turned to 1 the hand fully follows the box, when 0 then to returns to its original pose. You then constrain the box to the handle. There are adjustment controls to align the box to the handle and the hand to the box. Make adjustments till you get the movement you want. Holding hands is done the same way except constrain both hands to the prop and then as you move the prop back and forth it will look like the couple is swinging their hands in time.

This seems to work well for a hand to a crank. The adjustment of the prop controls the hand. If I use that hand and constrain the prop to any body part of another figure, the second figure is impossible to pose as I wish. I am trying to get the hand of the first figure to follow the movements of the second figure's body part, hand or otherwise.

Use the same setup. Turn IK on for the hand that needs to follow the second figure. Select the first figures hand. Object > Add Constraint ... and select whatever body part you want it to follow.

Lets say you want to have Figure 1 put their hand on Figure 2's hip as if they are dancing. Constrain the prop to Figure 2's hip and adjust the position to were you want it. You should then be able to move figure 2 around and the box follows the figures hip. Then Constrain Figure 1's hand to the box. Figure 2 moves box moves and Figure 1's hand moves.

I can get the box to follow a body part okay when I constrain the box to it, but if I constrain any body part to the box it gets distorted. I am using Michael M4's hand. It gets worse if I turn on IK. What am I doing wrong?

On the box/prop you will need to change the orientation to match up with the figures body part. The part that is being constrained to is the leader and the body part the follower. The follower will change its orientation to match the Leaders.

Best way to do this is to bring in the box and place it under the hand. Constrain the box the the hand and turn the value up to 1. watch how the box twists as it gets nearer. Set the constraint back to zero and adjust the box in the same direction until it no longer twists when the constraint is turned up to 1. Now use those values on your other box and the body part should not distort.

One final thing is that you CANNOT constrain one body part to another body part on the same figure as that causes a feedback loop as the part tries to find the target which is moving and another cycle begins again.

I still can not get this to work. Once I have constrained the box to the hip of figure 1 ( which works as you said ) I try to constrain the hand of figure 2 to the same box. The hand gets completely distorted. If the box is constrained to the hip of figure 1, I can set the constraint to 0 and move the box, but the hand of figure 2 is so distorted the I am unable to get it to return to the original shape. Your second explanation makes is sound like there should be 2 boxes. Also. do I change the constraint with the box selected, the hip or the hand?

OK sorry it has been a couple of days, but work has been busy.

Lets try this: You should constrain the hand of figure 1 to the hip of figure 2. TO readjust the hand of figure 1 you need to select at the top of the Pose Window figure 2 and under the second selection options under Groupings select the Constraint Grouping that belongs to figure 1 hand. Notice the settings for the constraint object. there is a lot of rotation to make the hand line up. Also do not adjust the hand on figure 1 as it gets its values from the constraint object. With this setup I can move figure 2 and the hand tracks the hip.

It works !!! I had to remember to turn on IK for the hand to make the arm follow it. Thank you so much for your help!