So in the first post of this thread I said this -

"Recently, I developed the idea that ground reaction forces in the stance leg can help produce vertical acceleration of the pelvis during gait which will in turn will accelerate the swing leg provided it has started on a downward arc . I feel that this might be an important part of gait and also and important part generating leg speed when it comes to kicking things like a football ."

Thanks to the helpful input of all who have contributed to the thread , I am now pretty confident that vertical accelerations of the pelvis play a major role in coordinating body segment movement during gait , with such accelerations feeding energy into the pendulums that are the swing leg and the arms .

Just a final thought . If you get someone to walk on a treadmill you will see their arms swing . Get them to put one hand in their trouser pocket , inhibiting the swing of one arm , and you will see the swing amplitude of the contralateral arm increase to maintain body segment coordination . Actually, you can see the same effect if someone is walking with a strap supported handbag . One arm/hand steadies the bag causing the other arm to have a greater swing amplitude .