What is the physical grounding of your character movement? Angry Birds has a ballistic launch with a clear starting point, a direction and a velocity; following a finger seems much more complex. What do you mean by “freeing” a path? Where does energy come from? How is it conserved as potential and kinetic energy and lost in collisions and attrition?
Also, do you mean to make puzzles about avoiding obstacles to avoid getting hurt or about hitting the right obstacles in the right way to achieve an objective?
As a reference, there's a game series called “The Incredible Machine” that focuses on very diverse objectives and silly Rube Goldberg style engineering (e.g. hamster wheel motors moving conveyor belts to move cheese to attract a mouse to attract a cat to step on a pressure plate) but offers a rich variety of simple physical interactions (bouncing and rolling balls, billiard balls that are unaffected by gravity and superballs that gain energy when they bounce, floating balloons with ropes and pulleys, walls and slopes, wind sources pushing lightweight objects…) that allow puzzles that are solved by, for example, dropping a bowling ball from a precise location to bounce on suitably placed wall sections until it reaches a target.