Total Reaction Force Research Articles

Reaction Force Analysis in Generalized Machine Systems

A method is developed which reduces the calculation of reaction forces for multi-degree-of-freedom, constrained, mechanical, dynamic systems to a process of accumulating a sum of terms representing inertial forces, applied forces, and Lagrange multiplier forces. This method results in an approach to reaction force calculations which is computationally more efficient than either virtual work or equilibrium when these methods are applied in conventional ways. The method is based on selecting a tree for the network being simulated in which the chords of the network correspond to revolute pairs (for two-dimensional systems). When such a tree is determined, Lagrange’s equation with constraint is used to represent the mechanical system. If the paths to the centers of mass and the paths associated with applied forces are developed from tree branches, the Lagrange multipliers are directly interpretable in terms of the total reaction forces at the chords of the network. These multipliers are obtained in the process of determining the system motion. The remaining reaction forces and torques are determined by a sequence of additions.

A Device for Measuring Mechanical Characteristics of Tyres on the Road

This paper describes a machine which measures the mechanical force and moment characteristics of pneumatic tyres moving over flat road surfaces. Development of interest in tyre force measurements is briefly reviewed, and the unique relationship of the Air Force-Cornell tyre tester to other tyre force-measuring equipment is indicated. The design evolution is discussed and the final configuration of mechanical, hydraulic, pneumatic, and electrical components is described in detail. The axle carrying the test tyre is supported at its ends by units which measure five forces. A sixth measurement, braking torque, is made simultaneously. These six measurements are used to compute total road reaction forces and moments, referred to any desired axes. The supporting mechanism permits the test tyre to be steered 30 deg. to either left or right, tilted (cambered) 30 deg. from the vertical to left or right, and vertically loaded with a force variable from zero to 3,000 lb. A braking torque of 13,000 in.-lb. can also be be applied. Electrical resistance strain gauges sense the forces and produce time histories on a recording oscillograph. The entire equipment is mounted on a 2 1/2-ton 6-wheel truck which can attain speeds up to 60 m.p.h. while testing tyres.