When kinematic control of robot manipulator is modeled as time-varying problems, control algorithms generated by solving time-varying problems perform well in the aspect of real-time control and control precision. However, conventional algorithms are based on relatively simple time-varying problems modeling and solving, and thus, it is difficult for them to solve more other problems while completing tracking task. In this work, the kinematic control of robot manipulator is first modeled as more complicated multilayered time-varying problem, which simultaneously formulates the tracking task and joint angle limits. Then, zeroing neural dynamics method is future investigated to find the equivalence of multilayers. Finally, three explicit solutions based on three discretization formulas are presented to solve the multilayered time-varying problem. The presented solutions not only complete the tracking task in real time with different precision, but also solve the problem of joint angle limits during the control process.