In this paper we derive a dynamic model of the delta robot and two formulations of the manipulator Jacobian that comprise a system of singularity-free, index-one differential algebraic equations that is well-suited for model-based control design and computer simulation. One of the Jacobians is intended for time-domain simulation, while the other is for use in discrete-time control algorithms. The model is well-posed and numerically well-conditioned throughout the workspace, including at kinematic singularities. We use the model to derive an approximate feedback linearizing control algorithm that can be used for both trajectory tracking and impedance control, enabling some assembly tasks involving contact and collisions. The model and control algorithms are realized in the open-source Modelica language, and a Modelica-based software architecture is described that allows for a seamless development process from mathematical derivation of control algorithms, to desktop simulation, and finally to laboratory-scale experimental testing without the need to recode any aspect of the control algorithm. Simulation and experimental results are provided.