Make a ball and sock joint model with a foam cup and foam ball. Use foam pieces similar in size so that the ball snugly fits inside the cup. Cut a wooden kabob stick or dowel rod in half. Attach one half of the rod to the bottom side of a foam cup by poking it through the foam. Attach the other half of the rod to the ball by poking it through to the center. Place the ball inside the cup to resemble the ball and sock joint.
Make a model of a hinge joint with a block of foam about the size of a brick. Draw a curved line on the short side of the block piece. Use a utility knife to carve the block into two pieces along this curve, so that one piece has a concave side and the other piece has a convex side. Fit the pieces together to resemble the hinge joint.
Make a model of a pivot joint with a plastic ring and plastic bottle. Cut the top off of the plastic bottle at the point where the bottle begins to curve toward the opening. Discard the bottom of the bottle. Place a plastic ring -- such as a teething ring -- on top of the bottle opening to resemble the pivot joint.