With many micromanipulator designs emerging in micro and nanosystem applications, the element of compliance in the mechanisms is gaining attention. Several designs consider motions limited in a plane for high accuracy and repeatability as needed in micro/nano manipulation applications. Extending this to a full spatial configuration with coupled motions of series and parallel linkages with flexure joints of 1-degree-of-freedom (DOF) and 3-DOF needs a systematic analytical approach. One such approach for compliance analysis is presented in this article for a mechanism designed at Indian Institute of Technology Kharagpur. To validate the analytical models, finite element analysis simulations are performed with the help of the Abaqus-6.14 software package. Following the successful validation, the effect of structural parameters on the performance is presented with the help of the analytical expressions. We explore the performance of the mechanism with different dimensions of flexures of a particular type. Results indicate that the design with dissimilar dimensional parameters can give superior performance.

In this paper, an analytical study of the kinematics and dynamics of Stewart platform-based machine tool structures is presented. The kinematic study includes the derivation of closed form expressions for the inverse Jacobian matrix of the mechanism and its time derivative. An evaluation of a numerical iterative scheme for an on-line solution of the forward kinematic problem is also presented. Effects of different configurations of the unpowered joints on the angular velocities and accelerations of the links are considered. The Newton-Euler formulation is used to derive the rigid body dynamic equations. Inclusion of models for actuator dynamics and joint friction is discussed.

This paper presents a model-based controller consisting of a feedback linearization scheme and a state-dependent proportional derivative (PD) controller adapted to a parallel flight simulator Stewart mechanism. This parallel robot is considered to emulate motions of highly maneuverable aircrafts, which require well-trained pilots. The simulations are based upon a reduced-model prototype built in order to verify kinematic design aspects and control laws. Indeterminacies in the mass distribution of the system will generally affect model-based controllers, necessitating compensation or the employment of robust control methods. Through introducing the pilot's sensorial feedback of acceleration, the pilot's behavior in giving commands is emulated via an optimization process, which tunes the controller coefficients accordingly. Stability of the designed control system is guaranteed via the Lyapunov approach. To further explore the system through perilous flight scenarios, three pre-designed maneuvers are selected as test cases. It is expected that closed-loop control tasks in which a pilot tracks a target, while at the same time the controller rejects disturbances and adapts itself to the pilot's progressive skills, are ameliorated through this arrangement. Numerical results show that the proposed method is found robust in the training process in conditions of parameters indeterminacy.

This paper investigates the trajectory tracking of a Stewart platform, which is a typical multi-input multi-output nonlinear system, with unmodeled dynamics, parameter uncertainties, friction, and unpredictable actuator faults. An adaptive vector sliding mode fault-tolerant control law is derived to ensure the system is insensitive to uncertainties and drive the state variable errors of the closed-loop system to converge to the origin. Moreover, novel adaptive laws are proposed to update the upper boundary of uncertainty according to the actual system state, which greatly reduces the chattering of sliding mode control. Furthermore, velocity signals are estimated by introducing a simple nonlinear observer, resulting in the proposed controller requiring position measurements only. Finally, numerical simulations illustrate the effectiveness of the proposed control scheme.

In this research, a Stewart parallel platform with rotary actuators is simulated and a prototype is tested under different operative conditions. The purpose is to make the robot robust against inertia variations considering the fact that different payloads of unknown size may be transported. Due to the complexity issued by expressing the equations of motion with independent variables, the governing equations are derived by Lagrange's method using Lagrange multipliers for imposing the kinematic constraints imposed on this parallel robot. Eliminating Lagrange multipliers by projecting the equations onto the orthogonal complement of the space of constraints, the equations of motion are transformed to a reduced form suitable for the purpose of controller design. The control approach considered here is based on a neuro-fuzzy interference method. As a first step, each revolute arm link are individually trained under different loadings and diverse maneuvers. It is purposed that once employed together, the links will have learned how to collaborate with each others for performing a common task. Training data are divided to several clusters by using a subtractive clustering algorithm. For every cluster, a fuzzy rule is derived so that the output follows the desired trajectory. In the last stage, these rules are employed by utilizing back propagation algorithms and the effectiveness of the neuro-fuzzy system becomes approved by performing multiple maneuvers and its robustness is checked under various inertia loads. The controller has ultimately been implemented on a prototype of the Stewart mechanism in order to analyze the reliability and feasibility of the method.

This paper presents a novel method to determine the workspace of parallel manipulators using a variant of the Firefly Algorithm, which is one of the emerging techniques in swarm artificial intelligence. The workspace is defined as a set of all the coordinates in the search space that are accessible by the parallel manipulator end effector. The workspace formulation of the parallel manipulator considered in this paper has actuated and passive joint displacements which values are limited by their physical constraints. A special fitness function that discriminates between accessible and inaccessible coordinates is formulated based on the joint limitations. By finding these coordinates using the proposed Firefly Algorithm, the workspace of the manipulator can be constructed. The proposed method is an easy-to-implement alternative solution to the current numerical methods for workspace determination. The method consists of two stages of operation. The first stage maps the workspace to find the initial results with a space filling approach, in which a number of coordinates in the workspace are identified. The second stage refines the results with a boundary detection approach which focuses on the mapping of the boundaries of the workspace. The method is illustrated by its application to determine the 2D, 3D, and 6D workspaces of a Gough--Stewart Platform manipulator. Furthermore, the method is compared with a more rigorous interval analysis method in terms of computational cost and accuracy.

This paper deals with the motion prediction and control of the macro–micro parallel manipulator system for a 500-m-aperture spherical radio telescope (FAST). Firstly, based on principles of parallel mechanism, a decoupled tracking and prediction algorithm to predict the position and orientation of the movable macro parallel manipulator is presented in this paper. Then, taken as the upper layer supervisory controller in the joint space of the micro parallel manipulator, the adaptive interaction PID controller utilizing the adaptive interaction algorithm to adjust the parameters of a canonical PID controller is discussed. In addition, the digital servo filters with feedforward are employed in the linear actuators as the lower layer controllers. Experimental results of a one-tenth scale FAST field model validate the effectiveness of the supervisory controller and the motion prediction algorithm.

The Stewart platform manipulator is a fully kinematic linkage system that has major mechanical differences from typical serial link robots. It is a six-axis parallel robot manipulator with a high force-to-weight ratio and good positioning accuracy that exceeds that of a conventional serial link robot arm. This study examines the dynamic equations and control methodology for a Stewart platform. Because manual symbolic expansion of Stewart platform robot dynamic equations is tedious, time-consuming, and prone to errors, an automated derivation process is highly desired. The main goal of this work is to present an efficient procedure for computer generation of dynamic equations for a Stewart platform manipulator. As MATLAB has a powerful signal processing toolbox along with symbolic processing capabilities and is widely used as a common technical computing environment in many universities and research laboratories, the objective of this study was to develop a MATLAB-based approach for symbolic computation for a parallel linked robot. Additionally, a computed-torque control methodology is utilized for such a structure. Simulation results demonstrate the effectiveness of the proposed control methodology.

This paper studies the static rigidity behaviour of a parallel manipulator with legs modelled as elastic members under axial loading. Structurally, a parallel module is more rigid compared to a serial module and is expected to take heavier payloads. Therefore, a guidance for design of such parallel manipulators is needed which leads to maximum rigidity over the workspace. In the present work, the authors propose the concept of the flexibility ellipsoid for a parallel system. Various scalar measures of rigidity are formulated on the basis of the proposed ellipsoid. An algorithm, involving multiple objective nonlinear programming technique, is implemented to decide upon some important design parameters of a generalised six degrees of freedom Stewart platform type parallel manipulator. It is observed that irrespective of the other parameters, parallel manipulators with the legs pairwise joined at the top platform possess the highest rigidity. Moreover, there exists certain kinematic dimensions for which the designed parallel system is completely free from all sorts of singularity.

Most of the calibration methods proposed for the Stewart platform require complex computation or low noise data for the platform's accuracy to be determined. They are not suitable for practical use in a production environment, where the measurement and calibration method should be simple and robust. Using an external laser measuring device to determine the actual accuracy of a Stewart platform, a practical and simple leg length compensating calibration method, that improves the accuracy of the Stewart platform by a magnitude of around 7, is proposed. The procedures and computation algorithms of the calibration method are shown.

A 6-DOF motion bed is proposed as a nonlinear robust observer to solve the forward kinematics problem of a Stewart platform. The stability of the estimation error dynamics is proved via Lyapunov stability analysis and the error dynamics shows practical stability. An observer design algorithm which tackles the nonlinearity and uncertainty both in the system and in the output is presented by a new arithmetic Riccati equation. The estimation performance for the algorithm is verified using both simulations and experiments. The equation employs the bounding condition computed from the platform dynamics.

A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot's Jacobian or mass matrix. A new discrete global optimization algorithm is also proposed to optimize either the GII or some local measure without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimal architecture for a planar haptic interface from both a kinematic and dynamic perspective and to choose the optimum geometry for a 6-DOF Stewart Platform. The algorithm demonstrates consistent effort reductons of up to six orders of magnitude over global searching with low sensitivity to initial conditions.

A calibration method for a Stewart platform has been developed as partof a project aimed at developing a calibration method for a Delta robot. TheDelta has 3 degrees of freedom (DOF) but is more complex than the Stewartplatform for calibration purposes because an extra link is inserted in eachkinematic chain between the base and the Nacelle member.