Multi-objective optimization of stiffness and workspace for a parallel kinematic machine

Radiotherapy (RT) enables a selective destruction of tumor cells, although the treatment area is limited to the irradiated volume. Any RT technique comes along with multiple sources of error, which can lead to a deviation of the dose that is applied to the patient. Phantoms—structures that replicate a human and include measurement technology to assess the applied dosage—are used to make such errors observable. Past RT-technologies assumed static tumors. Correspondingly, most existing phantoms comprise only static components. Nowadays, RT is at a transition stage toward techniques which explicitly account for physiological motion. These techniques require phantoms generating such motion. Consequentially, a demand for new kinds of manipulators, which operate with a RT-phantom, has come up and will further increase in the future. Key demands of such manipulators are among others, the generation of full rigid body motion, high acceleration, high stiffness, compactness, little weight, and easy portability. Another indispensable feature is the spatial separation of mechatronic components and phantom structure to ensure human equivalency of the latter. In this work, a new kind of parallel kinematic manipulator (PKM), which is tailored to the requirements of RT-phantom technology, is presented. The PKM consists of low cost standardized mechanical components and sets the target structures, which are located inside a human-equivalent area, into translational and rotational motion in three degrees-of-freedom (DOFs). Only a part of the end-effector is located within the human-equivalent area. All the remaining parts of the PKM are located outside that area. Two versions of the manipulator are presented in detail: their kinematics are derived and their kinetostatic properties are compared. This includes a workspace analysis and the analysis of the transmission behavior in general, meaning the influence of the most important design parameters on the performance. It can be shown that practical differences of both kinematics are negligible, while the modified version provides significant mechanical advantages. In conclusion, a first special purpose manipulator for application in the evolving field of RT-phantom technology is presented. The PKM, which employs a novel kinematic structure, provides higher suitability for its purpose than any other robotic system employed so far for the same purpose.

This article examines Genetic Algorithms to solve the forward kinematics problem applied to planar parallel manipulators. Most of these manipulators can be modeled by the tripod 3-RPR. The conversion of an equation system solving problem into an optimization one is investigated. Parallel manipulator kinematics are formulated using the explicit Inverse Kinematics Model (IKM). From the displacement based equation systems, the objective function is formulated specifically for the FKP using one squared error performance criteria. The proposed approach implements an elitist selection process where a new mutation operator for Real-Coded GA is analyzed. Experiments on a typical manipulator example shows the fast convergence of the proposed method.

Design optimization of a spatial six degree-of-freedom parallel manipulator based on artificial intelligence approaches

Parallel manipulators (PMs) are often used as parallel kinematic machines (PKMs), which are more accurate and have more payload capacity compared to their serial counterparts. Spherical joints are frequently used in the construction of PKMs; however, spherical joints have a unique physical constraint, known as cone angle limit, around their axis of symmetry. The present work investigates the effect of changing the orientation of the spherical joint symmetry axis (SJSA) on the kinematic performance of PMs. Workspace index, global conditioning index, kinematic conditioning index and global stiffness index are chosen as performance indices. It is found that changing the orientation of SJSA has a remarkable impact on the kinematic performance of PMs. Also, it is shown that considering the cone angle limits considerably affect the kinematic performance of PMs. To demonstrate the results, two PMs, namely 3-PRS (P, R, and S denote prismatic, revolute, and spherical joints, respectively) and 3-RPS manipulators with spherical joints with adjustable axis of symmetry orientation, are used. The effect of changing SJSA orientation on various performance indices is carried out, and optimal orientation values are determined. Genetic algorithm (GA) optimization technique and traditional method are used. The results obtained using the two methods matched very well. It is found that orientation of the SJSA is one of the important PMs optimization parameters that should be considered during the design process.

This paper presents a comparison study of two unique micro-motion parallel kinematic manipulators (PKM): a three degrees of freedom (DOF) micro-motion PKM and a 3-DOF micro-motion PKM with actuation redundancy. The 3-DOF micro-motion PKM has three linear-motion driving units, while the 3-DOF micro-motion PKM with actuator redundancy has four of these units. For both designs, the linear motion driving units are identical and both machines have the same passive link in the middle of the structure. The manipulator with actuator redundancy is designed to prevent singularity and to improve stiffness. The inverse kinematics and Jacobian of these two PKMs are analyzed, the stiffness properties are determined and global stiffness is optimized using genetic algorithm. A comparison of the global stiffness indicates that the 3-DOF micro motion PKM with actuator redundancy outperforms the one without actuator redundancy.

Mechatronic design of a 3 degrees of freedom parallel kinematics manipulator with integrated force plate for human balance evaluation and rehabilitation✰

The manipulator workspace denotes the work area of a manipulator and it is an important foundation of designing a robot. The workspace of a novel symmetrical 4-DOF 3-RRUR parallel manipulator is researched here based on the inverse solution. Five essential conditions of a point within the workspace of the manipulator are presented and the cause of the existence of each condition is given. According to the characteristics of this parallel mechanism and the geometrics, and based on the inverse kinematical solution of the mechanism, the reachable workspace under the five conditions is ascertained. The three-dimensional graph and its section graphs of the workspace are obtained. The thoroughness of the workspace of the manipulator is proved. The mechanism with the advantages of simple symmetric structure and large stiffness can be applied to the developments of four-dimensional force sensors, NC positioning platforms, parallel machine tools and micro-positional parallel manipulators. This work is with great significance to the practical application of the manipulator.

Dynamics simulation of parallel kinematic manipulators (PKM) and non-linear control methods require a precisely identified dynamics model and explicit generalized mass matrix. Standard methods, which identify so-called dynamic base-parameters, are not sufficient to this end. Algorithms for identifying the complete set of dynamic parameters were proposed for serial manipulators. A dedicated identification method for PKM does not exist, however. Such a method is introduced here for the large class of Delta-like PKM exploiting the parallel structure and making use of model simplifications specific to this class. The proposed method guarantees physical consistency of the identified parameters, and in particular a positive definite generalized mass matrix. The method is applied to a simulated model with exactly known parameters, which allows for verification of the obtained dynamic parameters. The results show that the generalized mass matrix, the acceleration, and the Coriolis, gravitation and friction terms in the equations of motion (EOM) are well approximated. The second example is a real 4-DOF industrial Delta robot ABB IRB 360-6/1600. For this robot, a physically consistent set of inertia and friction parameters is identified from measurements. The method allows prescribing estimated parameters, but does not rely on such data, e.g. from manufacturer or CAD.

The synthesis of three‐degree‐of‐freedom planar parallel manipulators is performed using a genetic algorithm. The architecture of a manipulator and its position and orientation with respect to a prescribed workspace are determined.The architectural parameters are optimized so that the manipulator's constant‐orientation workspace is as close as possible to a prescribed workspace. The manipulator's workspace is discretized and its dexterity is computed as a global property of the manipulator. An analytical expression of the singularity loci (local null dexterity) can be obtained from the Jacobian matrix determinant, and its intersection with the manipulator's workspace may be verified and avoided.Results are shown for different conditions. First, the manipulators' workspaces are optimized for a prescribed workspace, without considering whether the singularity loci intersect it or not. Then the same type of optimization is performed, taking intersections with the singularity loci into account. In the following results, the optimization of the manipulator's dexterity is also included in an objective function, along with the workspace optimization and the avoidance of singularity loci. Results show that the end‐effector's location has a significant effect on the manipulator's dexterity. © 2002 John Wiley & Sons, Inc.

Reconfiguration of a parallel kinematic manipulator with 2T2R motions for avoiding singularities through minimizing actuator forces

Photolithography is one of the core technologies of micro-nano fabrication. Recently, lithography technology is applied to diverse field of technologies. These technologies include MEMS (micro electro mechanical system) devices, FPD (flat panel display), and semiconductor industry. When it comes to the typical exposure process of lithography technology, photomask costs is occupying large portion of the optical system. So, how to reduce the cost of the mask and employing maskless lithography technology has become an important issue to engineers. Although there being both advantages and disadvantages, maskless lithography is a receiving substantial attention from engineers in the fileds of micro-nano fabrication. With the development of technology, low cost, flexibility, efficiency in the fabrication of device are in high demand in maskless lithography technology. How to generate line/space patterns is gaining considerable attention in terms of maskless lithography exposure process. In order to achieve the accurate alignments of numerous optical heads within a reasonable amount of tack time, installing autonomous position align micro parallel manipulator system in each optical heads required. Applied parallel manipulator that consists of four 2-DOF (degree of freedom) decoupled actuator gives chances to provide 6-DOF independence motion, and has strength in high accuracy. It is thus, this parallel manipulator is suitable for the experiment. This paper covers the follows: First, we reported the DMD (Digital Micro mirror Device)-based makless lithography system to introduce spot array method in maskless digital exposure process. Second, applying a redundant parallel micro manipulator and analyzing kinematic characteristic of the 4-[PP]PS parallel manipulator is described. After that, comparing benefits and drawbacks of 4-[PP]PS parallel and 4-DOF serial manipulator is covered. Third, proposing a suitable error model of the system and applying the genetic algorithm to alignment spot array concerning position correction. Finally, we designed experiment which has vision sensor and align unit to verify positioning algorithm. Simulation and experimental result will be shown with the regard to parallel manipulator can find the optimal solution based on genetic algorithm and carry out the problem of spot array alignment by reducing the position error of the system.

This paper presents a new multi-objective optimization method, which is inspired from the idea of non-dominated sorting genetic algorithm (NSGA) and genetic quantum algorithm (GQA). The GQA has been tested on well known test beds in single objective optimization and compared with the genetic algorithm (GA) in the lead author’s previous work [22]. This paper aims to apply the idea of GQA to multi-objective optimization (MOO). The developed method is called non-dominated sorting genetic quantum algorithm (NSGQA). The developed method is tested with benchmark problems collected from literature, which have characteristics representing various aspects of a MOO problem. Test results show that NSGQA has better performance on most benchmark problems than currently popular MOO methods such as the NSGA. The integration of GQA with MOO, and the systematic comparison with other MOO methods on benchmark problems, should be of general interest to researchers on MOO and to practitioners using MOO methods in design.

The hexapod is a parallel kinematic manipulator that is the minimum arrangement for independent control of six degrees of freedom. Advancing needs for hexapod performance, capacity and configurations have driven development of highly capable new actuator designs. This paper describes new compact hexapod design proposals for high load capacity, and corresponding hexapod actuator only mechanisms suitable for integration as structural motion elements in next-generation telescope designs. These actuators provide up to 90 000N load capability while preserving sub-micrometer positional capability and in-position stability. The design is optimized for low power dissipation and incorporates novel encoders direct manufactured with the nut flange to achieve more than 100000 increments per revolution. In the hexapod design we choose cardan joints for the actuator that have axis offsets to provide optimized stiffness. The additional computational requirements for offset axes are readily solved by advanced kinematic algorithms and modern hardware. The paper also describes the hexapod controller concept with individual actuator designs, which allows the integration of hexapod actuators into the main telescope structure to reduce mass and provide the telescope designer more design freedom in the incorporation of these types of motion systems. An adaptive software package was developed including collision control feature for real-time safety during hexapod movements.

This paper presents the design and analysis of a novel five degrees-of- freedom (DOF) parallel kinematic manipulator (PKM) for part-handling, sorting, general positioning, and robotic machining applications. The 2- R(Pa-IQ)RR, R(Pa-IQ)R manipulator has two rotational DOFs, one parasitic rotation, and three translational DOFs. In comparison with other 5- and 6- DOF PKMs, this PKM possesses three pairs of coplanar legs that contain nested kinematic chains, and it makes exclusive use of revolute and prismatic joints. The inverse kinematic analysis is a novel extension of the geometric (vector) method with the analysis of inner and outer kinematic chains. The forward kinematic analysis was solved using the Newton Raphson (NR) method. The results of the forward and inverse kinematic analyses were validated with SolidWorks ® and MATLAB ® simulations.

Parallel manipulator kinematics learning using holographic neural network models