Robotics vehicle-machines are designed to do a suitable and useful work in sustained equilibrium and non-equilibrium positions. The work done could be inspecting, transmitting or utilizing power supply to drive and orient desired amount of loads or elastic structures to a location at particular time. The configuration of robotics machine-vehicles is made up of several interconnecting components. The equilibrium and nonequilibrium positions of a robotics machine-vehicle consist of determining time delays in the elastic structures. During the operation of a robotics vehicle-machine, there is a continuous propagation of displacement time delays from one component to another. The time delays together with the state initial conditions of the robot vehicle-machine estimate the probability intervals for which the dynamic requirements are attained. Namely, (i) maintaining stability, (ii) balancing input-output responses and (iii) minimizing sensitivity levels during the operation of the robotics vehicle-machine. In this paper, we locate the displacement time delays in the elastic structures of the components of the robotics vehicle-machine. The displacement time delays will prevent the robotics vehicle machine from leaving the admissible performance index range. Quantify uncertainty and imprecise probability that the robotics vehicle-machine can sustain at operating equilibrium and nonequilibrium positions when the stress-strain relationships nonlinear and influenced by Wiener Process. At each one of the equilibrium and non-equilibrium positions, we will locate critical values of the component parameters that are pronoun to induce large uncertainty and imprecise probability. The infinite dimensional amplitude and frequency responses maintaining stability and reduce sensitivity dependent on sudden changes in the time delays will be determined.