The Franchot engine is a double acting Stirling engine with only two cylinders and freely controllable phase angle. The hot and cold cylinders of the Franchot engine can be directly heated and cooled and thus act as heaters/coolers. However, the cylinders are necessarily long and thin to increase the heat transfer area and hence the power. The long strokes result in long cranks and connecting rods which lead to large and unwieldy engines. In this contribution, the directly heated and cooled multi-cylinder Franchot engine is dynamically studied with a novel balanced compounding mechanism. Thus, the balanced compound Franchot engine would be more compact, cheaper and more efficient due to the removal of the rotational parts. The new mechanism includes a linkage between two connecting rods in a conventional Franchot engine for which, four pistons (an expansion, compression and two guiding pistons) move as one reciprocator. The influence of different engine parameters, such as number of cylinders, temperature, dead volume and reciprocator mass, on the new configuration is investigated. The possible phase angles for each number of cylinders are given. The balanced compound Franchot engine changes the order of piston motion so that the largest of these phase angles is obtained. The theoretical analysis shows that increasing the number of cylinders, dead volume and reciprocating mass reduces the frequency and increases the stroke; increasing the cylinder diameter increases the frequency and decreases the stroke; increasing the load decreases the stroke and slightly decreases the frequency; and increasing the temperature increases both the frequency and the stroke. Thus, different engine parameters can be used to maximise the power generation without the piston hitting the cylinder head. The dynamic load, which is a function of the speed, does not prevent the balanced compound Franchot engine from self-starting while static friction can prevent the engine from self-starting, especially if the pistons are around the mid-stroke point. The most promising configuration is the three-phase engine which has the lowest number of cylinders, preferable phase angle and phase shift of 120 degrees and potential for electricity generation and heat pumping.