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Yayın On the equilibrium of a rigid body suspended by a set of linear springs(John Wiley & Sons, 2000-08) Tokad, YılmazIn this paper an approach is described for determining equilibrium states of a rigid body suspended elastically in space by a set of linear springs. This system is considered as a two-terminal generalized spring with terminal across (translational and rotational velocities, V-G, omega(G)) and terminal through (terminal force and moment, f(G), m(G)) variables. The algorithmic approach used for the solution of six nonlinear and coupled equilibrium equations consists of two major steps. The first step is to assign an initial orientation to the rigid body which is represented by the transformation (rotation) matrix T(theta,n) and reduce the problem to the solution of force equations only through a computer program. This yields the position vector xi of a preselected point G on the rigid body. Although the terminal force f(G) becomes zero at this position, the calculated terminal moment m(G), in general, is not equal to zero. The second step is to try to determine the correct orientation of the rigid body based on an argument that the terminal moment should vanish. The same argument is also used for the solution of force equilibrium equations. These two steps are repeated several times until both f(G) and m(G) vanish simultaneously yielding an equilibrium state (xi,T(theta, n)). Application of the approach is illustrated through various examples. It is observed that, if there are nonstable equilibrium states of the system, then sometimes all possible physical equilibrium states may not be obtained with this approach.Yayın End-effector trajectory control in a two-link flexible manipulator through reference joint angle values modification by neural networks(Sage Publications, 2006-02) Öke, Gülay; İstefanopulos, YorgoThe basic difficulty in the control of flexible link manipulators stems from the fact that the link deflections cannot be controlled directly. Since the number of control inputs, applied by the actuators, is less than the total number of variables to be controlled, control approaches aiming at the suppression of deflections and vibrations are generally insufficient. Another possible approach is to determine new joint trajectories to minimize the error of the end-effector in the operational space. In this paper, a neural network is designed to compute incremental changes for the reference values of the joint angles to achieve successful tip tracking in the operational space. Tip position errors in the x- and y-directions are utihzed as inputs to the neural network. The cost function, which is minimized in training the neural network, is also chosen as the sum of squares of the tip position error in both directions. Joint angle control is provided by a PD controller. Simulations are carried out to evaluate the performance of the neural-network-based trajectory tracking method, and the results are depicted in both joint and operational spaces.Yayın On the kinematic of a 3-DOF Stewart platform(John Wiley & Sons Inc, 1999-02) Bürüncük, Kadri; Tokad, YılmazThe kinematic behavior of the Stewart platform has been discussed in the literature by many researchers. In the present article, a special form of the Stewart platform, namely, the 3-degrees of freedom platform with triangular shaped base and upper platforms, is considered by thoroughly deriving a new set of constraint equations which makes it possible to discover several new properties of the platform. Both the inverse and direct kinematic problems are discussed and a new approach for solution of the direct kinematic problem is described which gives all the real (physical) solutions.
