Just joined PF and my mind is completely shutting down on me. I need to design the base of a halogen desk lamp and am having a problem getting started. My biggest problem is finding the correct equation to use to begin calculating the numbers. It is a three dimensional problem. Can someone please help me with this. I have attached a pdf file of the diagrams and known information. The basics are that the base needs to be circular and angles α and β are measured horizontally regardless of their position.