Some Attempts to Exploit Centrifugal Force

Fig. 1  A mass m in a turning wheel

Offsetting

As the wheel of Fig. 1 turns with rotational speed ω, the mass m, at radius r, travelling at velocity v, experiences a centrifugal force of F  =  mv²/r  =  mω²r.  As a force, F is a vector quantity, whose line of action passes exactly through the wheel's center. If the line of action could be offset even slightly, as shown in Fig. 2,  F would exert torque on the wheel, accelerating its rotational speed.

Fig. 2  An offset centrifugal force vector

While it isn't possible to achieve a simple offset of centrifugal force like this, there are other possibilities. Let's now look at a few of them.


Splitting forces and torques

Fig. 3  Centrifugal force split into two equal forces and torques

Fig. 3 shows the mass centrally located on a bar, with vertical arms linking to other arms on the wheel's centerline, each with a torsion link (solid circle) to the wheel. 

The single, centrally-directed centrifugal force has now been split into four components: two torques and two forces which are no longer centrally-directed. Obviously the forces and torques balance out for this model, but could it be possible to find a case where there is some imbalance?


A lower arm reversed

Fig 4  Split forces and torques with a lower arm reversed

Fig 4 shows one of the lower arms reversed, so that it is attached to the wheel at a larger radius than the other arm. Here the effect of the left side force being exerted at a larger radius is balanced out by the higher force on the right side, and the torques being exerted in the same anticlockwise direction. There is no overall torque on the wheel.


Split torques turning in the same direction, with equal torsion links

Fig. 5  Split torques in the same direction. All torsion links are equal

Fig. 5 shows another linkage from the mass to the wheel.  If the model could be made stable with equal torsion links (solid circles) as shown, then both the left and right split forces would be equal to F/2, balancing out, yet the two torques would both turn the wheel anticlockwise. 

I made some silux models of this idea (below), all with 1m diameter wheels. The first one does have equal torsion links installed as shown in Fig. 5.

Fig. 6  Silux model of Fig. 5, with equal torsion links

Details:—
wheel mass: 100kg
all arm masses: 0.1kg
mass: 4kg

all torsion links: 50 N-m/rad
wheel speed 12.5 rad/s.

The model reaches the equilibrium position shown in Fig. 6, with no net torque on the wheel.



Split torques turning in the same direction, with unequal torsion links

Fig. 7  Silux model of Fig. 5, with unequal torsion links

This silux model was similar, except for the torsion link values:

torsion links left: 70 N-m/rad
torsion links right: 5 N-m/rad

wheel speed 12.5 rad/s.

This time, the model reaches the approximately symmetrical equilibrium position shown in Fig. 7, but once again there is no net torque on the wheel. The higher torque on the left side means there must also be a higher force on that side, and the two effects cancel out.



Split torques with torsion links only on lower arms

Fig. 8  Silux model of Fig. 5, with torsion links only on lower arms

This silux model was again similar, except that:

torsion links were installed between the arms: both 25 N-m/rad
only simple links were installed between upper arms and the bar.
torsion links lower arms to wheel: both 50 N-m/rad

wheel speed 12.5 rad/s. 

The model reaches the equilibrium position shown in Fig. 8. Note that there is no torque exerted on the lower arms, and hence on the wheel.


Other possibilities

Fig. 9  Both force and torque are exerted on the right of the wheel, tending to cancel out.
On the left, force is still exerted on the wheel, but torque is reacted by the carrier (blue)
which has rollers running in the fixed, circular earthed track (green).

There are obviously many other possibilities that could be investigated, such as having split forces and torques, both exerted on one side against the wheel, but with only the force on the other side exerted on the wheel, for example as shown in Fig. 9. Another option would be to have force and torque exerted only on one side, again with the force but not the torque acting on the wheel, as shown in Fig. 10.

Fig. 10  Here force acts only on the left of the wheel, with torque acting on the earthed track via the carrier.
The mass oscillates radially because of the torsion link, possibly together with a spring added between the mass and the wheel center, opposing the centrifugal force. This oscillation is intended to permit resetting of the carrier as required in the non-circular earthed track, when the mass is at its minimum radius, four times per revolution.

These possibilities, or something like them, could be worth further work; but overall I think it's unlikely that centrifugal force, by itself, can be exploited to give a net torque on a wheel.