KINEMATIC ANALYSIS OF A PISTON MECHANISM WITH A ROTATING CYLINDER: ANALYTICAL ANALOGY AND GRAPHICAL CONSTRUCTION OF ACCELERATION

The acceleration analysis of a piston mechanism with a rotating cylinder requires careful formulation of the geometric relations, since the standard procedure does not immediately provide a closed system for determining the angular acceleration of the rod. This paper shows that the problem can be treated in a didactically transparent way by using two instantaneous kinematic analogies: reduction to an eccentric slider-crank mechanism and introduction of an auxiliary four-bar linkage. The first analogy provides an analytical route to the required quantity without direct differentiation of a complex function, while the second enables a graphical interpretation of the normal, tangential and Coriolis acceleration components. It is also shown that, in the case of uniform rotation of the driving crank, the direction of the total acceleration of a characteristic point can be related to the initial geometry of the mechanism.