Easy way to create a simple animation and trace path of a point?
Easy is subjective, but using Solvespace may allow you to accomplish your objective. The included link has a section about three-quarters of the way down referencing the trace point feature of the program.
Solvespace is a multi-platform, free program that allows for parametric designs in 3D but will function fine for 2D projects such as this.

This image from the linked site shows a 4 bar linkage with length parameters applied.