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SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

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a b s t r a c tHexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

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Assuming a sinusoidal machining force, the forced vibration of a machine tools' hexapod table in different directions is addressed in the present study. A vibration model for the hexapod table is developed and the relevant explicit equations are derived. In the vibration equation of the table, the pods are assumed as spring-damper systems and the equivalent stiffness and damping of the pods are evaluated using experimental results obtained by modal testing on one pod of the hexapod table. The results of the analytical approach have been verified by FEM simulation. The theoretical and FEM results exhibit similar trends in changes and are close to each other. The vibration of the table in different positions has been studied for rough and finish machining forces for both down and up milling. The ranges of resonance frequencies and vibration amplitudes have also been investigated. The safe functional modes of the table in terms of its upper platform's position have subsequently been determined.

SUMMARYThe 3 degree-of-freedom Gantry-Tau manipulator with the addition of the spherical wrist mechanism which is called Gantry-Tau-3R is designed as a high-G simulation-based motion platform (SBMP) with the capability of generating the large linear and angular displacement. The combination of both parallel and serial manipulator in newly designed Gantry-Tau-3R mechanism improves the ability of the mechanism to regenerate larger motion signals with higher linear acceleration and angular velocity. The high-frequency signals are reproduced using the parallel part of the mechanism, and sustainable low-frequency accelerations are regenerated via the serial part due to the larger rotational motion capability, which will be used through motion cueing algorithm tilt coordination channel. The proportional integral derivative (PID) and fuzzy incremental controller (FIC) are developed for the proposed mechanism to show the high path tracking performance as a motion platform. FIC reduces the motion tracking error of the newly designed Gantry-Tau-3R and increases the motion fidelity for the users of the proposed SBMP. The proposed method is implemented using Matlab/Simulink software. Finally, the results demonstrate the accurate motion signal generation using linear model predictive motion cues with a fuzzy controller, which is not possible using the common parallel and serial manipulators.