Why does a radial engine need a master rod? Why can't slave rods be the only rods? Would this spider bearing (around 1:05 in the video) work for an IC engine, why or why not?
Having a master rod means that the bottom bearings of the connecting rods follow a fixed path throughout the cycle. If they are all attached to the crankshaft via a spider bearing it the spider bearing itself has an extra degree of freedom to rotate around the crank bearing, having a master rod constraints this rotation.
Because the con rod bottom bearings are centred at some radius from the centre of crank bearing they will exert a torque when the line of action of the cylinder is not on a direct line through the centre of both. The master rod resists this torque which is ultimately transmitted to the cylinder preventing the con rod bottom bearings from rotating around the centre of the crank bearing relative to the centreline of the master connecting rod.
Depending on the geometry this could potentially lead to collisions between the con rods and cylinder walls and is likely to waste power by making the cylinders fight against each other.
A master rod would not be required if the geometry of the engine is such that the torques on the con rod bottom bearings balance out naturally, this will depend on overall geometry, crank throw, stroke, number of cylinders etc.
I had the very same doubt, but the things got clear once I looked an animation https://upload.wikimedia.org/wikipedia/commons/f/f5/Radial_engine_timing-small.gif. Since the 2 plates where all the rods are attached isn't blocked on the crankshaft, but instead it's mounted on bearings, if you had all the rods on these 2 plates running on bearings, at any fire of any cylinder these 2 plates would try to rotate freely over the crankshaft and mess up the entire engine. So you need 1 fixed con-rod in order to avoid this and actually discharge the force on the crankshaft.
The geometry of the radial engine prevents all the rods from being directly connected to the crankshaft. All of the cylinders are in a single plane, thus the connecting rods are also in that same plane.