In this paper, time optimal trajectory tracking of redundant planar cable-suspended robots is investigated. The equations of motion of these cable robots are obtained as a system of second order differential equation in terms of path parameter s using the specified path. Besides, the bounds on the cable tensions and cable velocities are transformed into the bounds on the acceleration and velocity along the path. Assuming bang-bang control, the switching points in ṡ2−s plane are obtained. Then the cable tensions are found in terms of path parameter and, subsequently, versus time. The proposed approach is validated and the effect of the number of superfluous cables on the value of minimum time is studied. The next notable challenges include time optimal path planning of cable-suspended robots. By developing a hybrid genetic algorithm and bang-bang control approach, the minimum motion time from initial state to final one and also the corresponding path can be found. The optimum path is the one that minimizes traveling time from initial state to final one, while not exceeding the cable tensions and cable velocities limits, without collision with any obstacles.

Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires − based on the Gurtin-Murdoch model − and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkinbased projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

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