This idea is for a toy which is deliberately designed to look
like the motor should just spin without moving the car
forward... but in fact, the toy moves quite well, even on
carpet.
The toy has eight wheels, four top and four bottom, and
can work either side up. None of the wheels is directly
motor-driven, instead each wheel merely has a ratchet and
pawl (or perhaps a sprag clutch), so it can spin forwards
but not backwards.
There are four parallelogram shaped linkages, two top and
two bottom, each linkage having two long segments, going
across the toy, and two short segments, parallel to the
sides of the toy.
Each short segment holds one wheel. Each long segment's
midpoint is attached to the chassis with a pivot. A spring
or rubber band pulls each linkage towards it's "neutral"
position, so that the wheels are less likely to hit the sides
of the chassis.
The two front linkages and the two rear linkages are
mirror images of one another, so I'll only describe the
front.
The front top and front bottom linkages are attached to
one another via a differential gear and a reversing gear.
When the middle of the differential is turned, the two
linkages move from being parallel to one another, to
forming an "X" shape.
(The reversing gear could be omitted, which would make
the toy simpler, but it would vibrate more, since turning
the differential would arrange the two linkages into a "/"
or "\" instead of an "X".)
The differential is not turned by a gear or a pulley, but
rather by a crank or lever.
Each of the toy's two levers are pushed and pulled by
connecting rods. The two connecting rods are attached to
the cranks of a single crankshaft. One end of the
crankshaft goes to the motor, the other protrudes from the
toy, and has a manually turn-able crank for playing with.
The two cranks that hold the connecting rods should be at
an angle to each other, so that when one lever is at the
forward-most or rear-most position, the other will be at
it's midpoint. Similarly, when the two front linkages form
an "X", the two rear linkages will be parallel to each other,
and vice versa.
When the toy is placed on a surface, and the hand-crank is
slowly turned, the bottom linkages won't move, but the top
ones will.
Children's logic might suggest that turning on the battery
powered motor will accomplish nothing but make the top
bits move faster...
In fact, as the top parts speed up, the bottom parts come
to life too!
The faster the top parts go, the more strongly the bottom
linkages twist.
And since the bottom linkages have ratcheting wheels on
them, the whole toy will move forwards.
Why does it work? It's a mystery!
I know why it works, and you, reading this, also might, but
what age child could identify the forces of physics
responsible?
If advertising jingle is needed, "The Marvelous Toy" comes
to mind.