This case study discusses the interpolation of minimum-jerk robot joint trajectories through an arbitrary number of knots using a hard-wired neural network. Minimum-jerk joint trajectories are desirable for their similarity to human joint movements and their amenability to accurate tracking. The resultant trajectories are numerical functions of time. The interpolation problem is formulated as a constrained quadratic minimization problem over a continuous joint angle domain and a discrete time domain. Time is discretized according to the robot controller rate. The outputs of the neural network specify the joint angles (one neuron for each discrete value of time) and the Lagrange multipliers (one neuron for each trajectory constraint). An annealing method is used to prevent the network from getting stuck in a local minimum. We show via simulation that this trajectory planning method can be used to improve the performance of other trajectory optimization schemes.