Pure Graphical Approach of Torque Computation

This paper presents a foundational reformulation of torque calculation for planar systems through a purely graphical methodology. Moving beyond standard algebraic computation, the technique utilizes classical Euclidean tools a straightedge and compass to determine both the magnitude and direction of a resultant torque. The theoretical core is formalized in two geometric lemmas. The first lemma establishes an exact equivalence between torque magnitude and the area of a representative right triangle. The second lemma derives a summation procedure, proving that projecting these triangles onto a common reference base allows the net torque to be expressed as the product of that base and a total constructed height. This reduces the entire summation process to a deterministic sequence of constructive geometry steps. The method is rigorously validated by applying it to a case study within a precise computational geometry environment. The graphical result is shown to be in exact Boolean agreement with the standard numerical cross-product solution. This approach offers significant didactic value by providing an intuitive visual synthesis of torque superposition, bridging a key conceptual gap in foundational machine dynamics education.

کلیدواژه ها:

graphical statics ، torque summation ، Euclidean construction ، planar dynamics ، geometric mechanics