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Design and optimal control of a dual-stage Stewart robot is performed in this paper using sequential optimal feedback linearization method considering the dynamics of the jacks. Considering the limited length of the jacks, the possible dynamic workspace of this robot is extremely limited. Dual-stage platform version of this robot is designed and proposed in this paper to improve this limitation. As a result, the dynamic workspace of the robot is increased by increasing the degrees of freedom (DOFs) of the system. Modeling and dynamics of the new proposed system are developed considering the dynamics of the jacks. Besides, the robot is controlled with the highest accuracy and the lowest energy using an optimal control strategy based on Feedback-Linearized Quadratic Regulator (FLQR). Two sequential controlling loops are employed for simultaneous control of the joint space and work space of the robot. The efficiency of the proposed manipulator toward increasing the workspace of the robot and also the...

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method.

Maximizing the singularity-free workspace of parallel manipulators is highly desirable in a context of robot design. So far, no work has been found to address the maximal singularity-free orientation workspace over a position region. In practice, this type of workspace is interesting because a mechanism often works in a range of positions. This work focuses on the Gough–Stewart platform. An optimal position at which the mechanism holds the maximal singularity-free orientation workspace is determined. This optimal position lies on the line which is perpendicular to the base and passes the centroid of the base. Considering the symmetry, a parallelepiped with centre at the determined optimal position could be an interesting working position region for the Gough–Stewart platform. Two algorithms are presented to compute the maximal singularity-free orientation workspace over such an interesting position region. An example is provided for demonstration.

A novel method is proposed for real-time solution of direct kinematics problem of Stewart platform (SP) using six measurements on three legs’ joints consisting of the rotations of three legs in two directions. After the application of the method on a laboratory sample SP, it is observed that the method is preferable to the conventional method that uses the length measurements of all six legs, in the grounds of industrial applicability. It is due to simpler implementation, less expense, easier maintenance, and stress-free assembly. The algorithms of both forward and inverse kinematics are fully derived based on geometric relationships between the platform states and the measurement data. The sensitivity to the measurement errors is analyzed theoretically and is applied through a computer simulation to several configurations of the sample SP which are uniformly distributed in the workspace. The variances of measurement errors for those configurations are compared between the conventional and proposed method...

This article describes the development process of a horseback riding simulator capable of generating a close to natural riding sensation. The development process started with 6-DOF motion measurement of the dynamics of the rider’s saddle during riding. Six-dimensional measurements during riding are required to fully understand the character of the saddle dynamics during different gaits. The measured quantities, i.e. translation accelerations and angular velocities, were transformed and filtered to form position references for a hydraulic Gough–Stewart platform. The presented novel motion measurement method is easy to use and makes it possible to measure gaits of several individual horses in a short time. It also provides a straightforward approach to produce motion data for the motion platform. In the second phase of the study, an artificial horse body made of glass fiber was mounted on the motion platform. The developed simulator realizes all three basic gaits walk, trot, and gallop. The rider is able to...

A parallel mechanism is a multi-legged kinematic structure with actuators fixed on the base. In recent years, parallel mechanisms have been implemented in haptic devices due to their benefits, such as high rigidity, high output force, high accuracy and high backdrivability. Multi-d.o.f. haptic devices with rotational motion have become increasingly important as haptic applications have become diversified (e.g., in surgical training). However, typical multi-d.o.f. parallel mechanisms (e.g., Stewart platform and HEXA) have limitations on the working area for rotational motions. A multi-d.o.f. haptic device can be designed by stacking the translational and rotational mechanisms by decoupling these motions. However, this dedoupling can have an adverse effect on inertia because of the weight of the stacking mechanism. Eventually, the operability of the device deteriorates. Therefore, a parallel mechanism with both a translational and rotational multi-d.o.f. structure can effectively apply the full advantages o...

When performing femur fracture reduction surgery, both the patient and surgeon are exposed to a great amount of radiation, which is harmful to their health. In order to reduce such radiation from the usage of an image intensifier, various robots have been proposed for femur fracture reduction surgery. Most of these robots are based on serial architecture. The low transportable load and poor accuracy are both inherent in serial robots, which makes them inappropriate for femur fracture reduction. Some parallel robots based on the 'Stewart platform' have also been developed for femur fracture reduction, but their restricted workspace limits their applicability and accessibility. To balance the accuracy, payload and workspace, a new robot system is reported in this paper. The proposed robot system consists of a 2-d.o.f. device and a 6-d.o.f. hybrid robot. The 2-d.o.f. device is used for distraction, which requires a very large force. The hybrid robot is used to manipulate a bone fragment for alignment and fix...

In this paper, the dynamics formulation of a general Stewart platform manipulator (SPM) with arbitrary geometry and inertia distribution is addressed. Based on a structured Boltzmann–Hamel–d'Alembe...

In this paper, a kinematic optimal design of a new parallel-type rolling mill based upon two Stewart platform manipulators is investigated. To provide the end-effector (work roll) with sufficient d.o.f. and to achieve the structural stability of each stand, a parallel manipulator with six legs is considered. The objective of this new parallel-type rolling mill is to pursue an integrated control of the strip thickness, strip shape, pair-crossing angle, uniform wear of the rolls and strip tension. By splitting the weighted Jacobian matrices into two parts, the linear velocity, angular velocity, force and moment transmissibilities are analyzed. A manipulability measure, as the ratio of the manipulability ellipsoid volume and the condition number of a split Jacobian matrix, is defined. The two kinematic parameters, the radius of the base and the angle between two neighboring joints, are optimally designed by maximizing the global force manipulability measure defined in the entire workspace. The maximum exerti...

In order to make a simulation more realistic, motion base simulators provide users with inertial cues, exerting linear accelerations and angular rates on the mock-up vehicle, in addition to the mor...

In this paper, impacts at the joints of a closed-chain mechanism are modeled and analyzed. It is assumed that a Stewart platform is attached to one end of a spacecraft to be utilized as a docking platform and the spacecraft docks with another spacecraft. When the spacecrafts dock with each other, impact will rise at the docking point and the impact is absorbed by the docking platform. Although the impact at the contact point is very large, most of the impact is absorbed by the docking platform and negligible impact is transmitted to the spacecraft. The docking platform can absorb the shock by inertial effect, not by damping or friction. To show this, modeling of the internal impulses at the joints of a multi-body system is introduced and the internal impulses of the docking platform are analyzed by the modeling method.

Manufacturing tolerances, installation errors and link offsets contaminate kinematic parameters of a nominal platform kinematic model. Since the platform controller determines the length of the leg...