Gene therapies for heart failure have emerged in recent years, yet they lack an effective method for minimally invasive, uniform delivery. To address this need we developed a minimally invasive parallel wire robot for epicardial interventions. Accurate and safe interventions using this device require control of force in addition to injector position. Accounting for the nonidealities of the device design, however, yields nonlinear and underconstrained statics. This work solves these equations and demonstrates the efficacy of using this information in a parallel control scheme, which is shown to provide superior positioning compared to a position-only controller.