The object is simple: Keep the stylus in alignment as the record groove radius decreases and the needle moves. But perfect aligmment of this delicate moving contact point isn't so simple. Some use straight arms, others use "S" curved and other shapes. These cause the needle movement to form an arc. So some use linear tracking mechanisms to avoid that.

What geometry is involved in getting the best alignment? What are the best shapes and why? What tables use(d) them?