In this paper, for handling general minimum-effort inverse-kinematic problems, the nonuniqueness condition is investigated. A set of nonlinear equations and inequality is presented for online nonuniqueness-checking. The concept and utility of primal neural networks (NNs) are introduced in this context of dynamical inequalities and constraints. The proposed primal NN can handle well such a nonlinear online-checking problem in the form of a set of nonlinear equations and inequality. Numerical examples demonstrate the effectiveness and advantages of the primal NN approach.