Read above how the bike works ...

Of course -- like riding a bike --

I thought we wanted to skip the higher maths.

Will it be tensor equations next?

If I have your and Dan's description of the exercises right you are basically doing drills in using the joints' tensions as a kind of analog vector abacus. My issue is not with your method of computation or arrival at resultant, but the formal structure of the solution that you intend to compute.

If any component of your vector sum is parallel to and of opposite sign to the attacking vector you are addressing, you create one of two things:

1) If parallel but offset, a force couple in the plane (and either rotation or torque (if you apply countering leverage moment)), or

2) If parallel and in-line, a linear resisting thrust.

The principle of juji tells me that aikido technique is applied without any component of force in-line and directly resisting. Additive is permissible in linear parallel but not negative. A negative parallel componet of force (irimi) is not allowable unless it induces rotation (tenkan), ie. - is offset and forms a couple and thus potential rotation. Perpendicular components are allowed to directly engage to counter as they originate in rotation (tenkan). Negative parallel components (irimi) must be allowed to engage free of resisting moment or torque against the couple that results. Thus, are the two fundamental priniciples linked in my mind.

Potential rotation can be converted gyrodynamically if angular momentum in a complementary (90 degree) plane can be developed. (See the bike again). It can also develop torque if reaction force is allowed to develop. Axial torque resistance is the weakest aspect of almost any structure. As I interpret this, Aikijujtsu may well allow for the provocation and exploitation of that damaging axial torque -- and thus ground reaction is certainly in play as the reaction forms that torque against the rotation potential that is developed.

Aikido, in my mind, would interpret the sensation of developing torque as reaction or resistance, and once provoked, would shift juji (90 degrees) to convert that rotation potential (tenkan)or to initate further positive offset rotation (irimi) in a complementary plane.