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Below is a solid works model of our initial design. So that the ball is carried by the mechanism the black link is on the plane of the lower half of the ball while the pink and green links share the plane of the upper half of the ball. This allows the black link to occupy the same planar space as the pink and green links. We hoped this would allow for a smooth transfer of the ball between links. This was our largest concern. We decided to laser cut these links out of sheets of 1/8" acrylic. This gave us very accurate link lengths and smooth surfaces. For the joints we used simple screws and lock nuts. This along with washers for spacers to avoid acrylic on acrylic friction gave us great joints. With almost no friction from the joints the motion was smooth and easy meaning less torque is required from our motor.
The issue with this design was that the small indentions were not sufficient to hold the ball securely. We couldn't make the indentions deeper because then the transfer between the links would lock up. We decided to try a different approach.