An approach for calculating the effective workspaces of parallel mechanisms has been considered in this paper. The effective workspace is a set of reachable by the end-effector points, where an important parameter (or parameters) from the point of view of operation is not higher than critical. In this article, the speed and torque in the drive and the stiffness of the mechanism are considered as such parameters. An approach to determining the appropriate effective workspace is presented for each parameter. The optimization process, which is based on presented methods, allows one to choose basic technical solutions of the designed robot: the links (lengths and cross-sections), the drives, and types of hinges, which guarantee its operability at the specified operational characteristics. Case studies of a delta robot with four degrees of freedom and a planar five-bar mechanism are presented for testing these approaches. The presented methods are of great practical importance because it uses movement parameters or operational characteristics that are decisive for this mechanism and have clear physical meaning.

This paper presents a new combined 9-DOF [3R-3R-3R] parallel architecture to perform the object catching in the real-time scenario. The architecture design is intended to carry heavy payload objects for the catching. This paper covers modelling the new architecture, kinematics, and dynamic analyses to compute torques/forces at the actuators. The simulation of kinematic and dynamic analysis in MATLAB. Vision sensors, encoders, PID controller, and current limiting are used to perform object catching. The architecture is the only delta robot application designed to catch regular-shaped objects in real-time scenarios.

This paper proposes a vision-based kinematic analysis and kinematic parameters identification of the proposed architecture, designed to perform the object catching in the real-time scenario. For performing the inverse kinematics, precise estimation of the link lengths and other parameters needs to be present. Kinematic identification of Delta based upon Model10 implicit model with ten parameters using the iterative least square method is implemented. The loop closure implicit equations have been modelled. In this paper, a vision-based kinematic analysis of the Delta robots to do the catching is discussed. A predefined library of ArUco is used to get a unique solution of the kinematics of the moving platform with respect to the fixed base. The re-projection error while doing the calibration in the vision sensor module is 0.10 pixels. Proposed architecture interfaced with the hardware using the PID controller. Encoders are quadrature and have a resolution of 0.15 degrees embedded in the experimental setup to make the system closed-loop (acting as feedback unit).

This paper aims at shedding lights on two approaches that were recently proposed for the constraint wrench analysis of robotic manipulators. Both approaches benefit from the Newton–Euler equations, screw notations, and constraint transformation matrices (CTM) to cope with the inverse dynamic problem of multibody systems. In the first approach, which is called the joint-based method, the constraint transformation matrices are derived directly from the kinematic constraints which are imposed on the rigid links by kinematic pairs. In the second approach, which is referred to as the link-based method; however, the constraint matrices are obtained based on the wrench transfer formula of each rigid link. In this study, by resorting to the definition of reciprocal screws, the former methodology is further enhanced to a new version as well. Moreover, based on the proposed modified joint-based CTM, constraint forces and moments distribution indices are introduced. The three constraint wrench analysis methodologies, two joint-based and one link-based, result in different CTMs and set of equations as well, which will be discussed in detail. In the end, on two case studies, a spherical four-bar linkage and a Delta parallel robot, the pros and cons of all three constraint wrench analysis methodologies are discussed, and the proposed indices will be examined. The numerical results reveal that, although all three methods identically compute the magnitude of the applied and constraint force and moment vectors, the joint-based approaches do not report the constraint components with respect to a specific coordinate frame. Moreover, it is shown that the proposed indices can approximately predict the constraint forces and moments distribution at joints, which can be used as force transmission indicators in multibody systems.

This paper introduces a novel kinematic of a four degrees of freedom (DoFs) device based on Delta architecture. This new device is expected to be used as a haptic device for tele-operation applications. The challenging task was to obtain orientation DoFs from the Delta structure. A fourth leg is added to the Delta structure to convert translations into rotations and to provide translation of the handle. The fourth leg is linked to the base and to the moving platform by two universal joints. The architecture as well as the kinematic model of the new structure, called 4haptic, are presented. Comparisons in terms of kinematic behavior between the 4haptic device and the existing device developed based on spherical parallel manipulator architecture are presented. The results prove the improved behavior of the 4haptic device offering a singularity-free useful workspace, which makes it a suitable candidate to tele-operated system for Minimally Invasive Surgery. The dimensions of the 4haptic device, having the smallest workspace containing a prespecified region in space, are identified based on an optimal dimensional synthesis method.

This paper addresses the problem of optimal mechanisms design, for the geometric structure and control parameters of mechanisms with complex kinematics, which is one of the most intricate problems in contemporary robot modeling. The problem is stated by means of task requirements and performance constraints, which are specified in terms of the end-effector's position and orientation to accomplish the task. Usually, this problem does not fulfill the characteristics needed to use gradient-based optimization algorithms. In order to circumvent this issue, we introduce case studies of optimization models using evolutionary algorithms (EAs), which deal with the concurrent optimization of both: structure and control parameters. We define and review several optimization models based on the workspace, task and dexterity requirements, such that they guarantee an adequate performance under a set of operating and joint constraints, for a Delta parallel manipulator. Then, we apply several methodologies that can approximate optimal designs. Additionally, we compare the EAs with a quasi-Newton method (the BFGS), in order to show that the last kind of methods is not capable of solving the problem if the initial point is not very close to a local optimum. The results provide directions about the best state-of-the-art EA for addressing different design problems.

This paper addresses the dimensional-synthesis-based kineto-elastostatic performance optimization of the delta parallel mechanism. For the manipulator studied here, the main consideration for the optimization criteria is to find the maximum regular workspace where the robot delta must posses high stiffness and dexterity. The dexterity is a kinetostatic quality measure that is related to joint's stiffness and control accuracy. In this study, we use the Castigliano's energetic theorem for modeling the elastostatic behavior of the delta parallel robot, which can be evaluated by the mechanism's response to external applied wrench under static equilibrium. In the proposed formulation of the design problem, global structure's stiffness and global dexterity are considered together for the simultaneous optimization. Therefore, we formulate the design problem as a multi-objective optimization one and, we use evolutionary genetic algorithms to find all possible trade-offs among multiple cost functions that conflict with each other. The proposed design procedure is developed through the implementation of the delta robot and, numerical results show the effectiveness of the proposed design method to enhancing kineto-elastostatic performance of the studied manipulator's structure.

This article deals with the kinematic calibration of the Delta robot. Two different calibration models are introduced: The first one takes into account deviations of all mechanical parts except the spherical joints, which are assumed to be perfect (“model 54”), the second model considers only deviations which affect the position of the end-effector, but not its orientation, assuming that the “spatial parallelogram” remains perfect (“model 24”). A measurement set-up is presented which allows to determine the end-effector's position and orientation with respect to the base. The measurement points are later be used to identify the parameters of the two calibration model resulting in an accuracy improvement of a factor of 12.3 for the position and a factor of 3.7 for the prediction of the orientation.