An Engine with Isochoric Combustion has pistons arranged within cylinders, connecting rods connected to the pistons and to upper joints of triangle links, and a crankshaft with crankpins offset from the centerline of the crankshaft by crank arms. The triangle links are connected to the crankpins at additional joints of the triangle links. Radius links are pivotally connected to the engine by pivot pins at one end and to the triangle links at a further joint of the triangle links at their other end. By way of geometry of the linkages defined by the crank arms, the triangle links, the radius links, and the connecting rods, and by way of the relative positions of the crankshaft, the cylinders, and the pivot pins, during a crank angle segment, the Cylinder Volume during the combustion event is characterized by an extended dwell.