(Lagrangian mechanics) Determining generalized coordinates/constraints.

Lavabug

Does anyone have any tips on how to properly determine the degrees of freedom in simple mechanical systems? I've done many problems but I often encounter a new one (or make one up myself) where I can't seem to get the proper number of generalized coordinates down right. Things like coupled beads on wires, hoops, thompson-tait pendulum...Done pretty much all the classic Lagrangian kinematics problems found in several textbooks but I know my prof is more creative than that. ;) I need something to hone my skills.

I often find 3-D problems easier than 2-D since you're given the holonomous constraints straight away(ie some relation between cylindrical coordinates or the equation of a paraboloid), so you know how many generalized coordinates you have via s = 3n -j, (n particles, j equations of constraint)