The theory of the torque balance method for azimuthal anchoring energy meas
urements is investigated in detail under a general case of anchoring streng
th relationships between two substrates and a generalized relationship equa
tion is deduced. As an example, azimuthal anchoring energies of several pol
yimide (PI) materials in magnetically aligned twisted-nematic (TN) cells ar
e determined and the experimental results are discussed.