Preparations for the anapole measurement in Fr indicate the possibility of performing a similar measurement in a chain of Rb. The sensitivity analysis based on a single-nucleon model shows the potential for placing strong limits on the nucleon weak interaction parameters. There are values of the magnetic fields at much lower values than previously found that are insensitive to first-order changes in the field. The anapole moment effect in Rb corresponds to an equivalent electric field that is 80 times smaller than in Fr, but the stability of the isotopes and the current performance of the dipole trap in the apparatus presented here are encouraging for pursuing the measurement.