I'm researching and experimenting an efficient way to animate a character in After Effects 10.5.0.253 with bendable knees and elbows, but all the common practices use rounded elbows and knees when i need them to be sharp points. The two methods I've research are the IK and puppet tools but all methods don't keep a sharp point constantly without leaving a gap or a rounded joint to close gap. The only tedious solution I've been able to come up with is to create the joint movement with either of the two methods above and then key frame a pointed knee and elbow rectangular sleeve with an added two points to bend and create sharp points. Any other solutions that are less tedious?
Have you tried lowering the polygon count on the puppet tool? or maybe you could leave gaps since you arnt going for a realistic loook/
Stylistic decisions sometimes need to be modified to meet the available technology or skills of the animator.
I do not completely visualize your problem but you can explore parenting and use that function to nail a small pointy shape layer to track the pivot points.
Hope you figure it out, interesting challenge.