Apply fuzzy interpolation method to calibrate parallel machine tools

In this paper, neural networks are presented to solve the inverse kinematic models of continuum robots. Firstly, the forward kinematic models are calculated for variable curvature continuum robots. Then, the forward kinematic models are implemented in the neural networks which present the position of the continuum robot’s end effector. After that, the inverse kinematic models are solved through neural networks without setting up any constraints. In the same context, to validate the utility of the developed neural networks, various types of trajectories are proposed to be followed by continuum robots. It is found that the developed neural networks are powerful tool to deal with the high complexity of the non-linear equations, in particular when it comes to solving the inverse kinematics model of variable curvature continuum robots. To have a closer look at the efficiency of the developed neural network models during the follow up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations. It is noteworthy to say that the developed models are a needed tool for real time application since it does not depend on the complexity of the continuum robots' inverse kinematic models.

The contour error cross-coupling control is very important to improve contour accuracy for the five-axis computer numerical control machine. The change in cutter orientation can cause the nonlinear motion of cutter tip, so the contour error calculation and compensation are very complex. For the five-axis computer numerical control machine with dual rotary tables, the forward kinematics model and inverse kinematics model are set up, and the influence laws of feed axis deviation to cutter tip deviation and cutter orientation deviation are studied. Then the simple and accurate calculation models for cutter tip contour error and cutter orientation contour error are established. Finally, the novel contour error cross-coupling control method based on kinematics model is developed. The experimental results show that the developed method can effectively improve contour accuracy of the five-axis computer numerical control machine.

This paper took a 3-UPS Parallel Machine Tool (PMT) as the object of research; it mainly introduced the process of establishing the compensation strategy for this PMT. Firstly the kinematics equations on driving chain and constraint chain was established on the basis of kinematics analysis. Then according to the structural characteristics and the results of kinematics analysis, the error compensation strategy of feedback correction type with the semi-closed loop control mode was used in the error compensation for this PMT by the method of installing respectively the encoders on the each joint of parallelogram mechanism, namely the compensation way of “parallel driving and series feedback” was adopted. Finally this paper has also deduced the theoretical model of error compensation. The research results in this paper provided a theoretical basis for realizing error compensation of this PMT, and had important practical significance for improving machining precision of PMT

A novel 6-SSP parallel machine tool and a novel 4SPS+UPU parallel machine tool are presented, and a novel CAD approach is proposed to machine a 3D free-form surface in its normal direction by using the two parallel machine tools. First, by adopting the CAD geometry constraint and dimension-driving technique, the simulation mechanisms of a 6-SSP parallel manipulator with 6-DOF and a 4SPS+UPU parallel manipulator with 5-DOF are created. Second, a 3D free-form surface and a guiding plane of tool path are constructed above the moving platform of the two simulation mechanisms. Third, the tool axis of simulation parallel machine tool is retained perpendicular to the 3D free-form surface. In the light of two prescribed tool paths, the driving limbs and the pose of the moving platform of parallel machine tools are solved automatically and visualized dynamically.

A 5-Degree of Freedom (DOF) 5-UPS/PRPU fully parallel machine tool (PMT) was introduced. Based on the original edition of CNC system, the concise motion control algorithm was deduced by analyzing the identical feature between two Euler angles of 5-UPS/PRPU PMT and two swing angles of conventional 5-axis cutter swing machine tool. Then by using the formula of the inverse kinematic solution of the PMT, the length of the driving axis in the joint space can be calculated. The new CNC system software based on this algorithm was developed and it has been applied successfully to the 5-DOF PMT in our laboratory.

Parallel kinematic machines (PKMs) have been attracting attention in research institutes as well as in the machine tool industry because of their structural rigidity due to their closed kinematic loops and their conceptual capabilities in high dimensional accuracy. During performance evaluation of the first prototypes of parallel machine tools, it turned out that their accuracy has not yet reached industrial application level. Against this background, the accuracy behaviour of a hexapod milling machine, located at the Laboratory for Machine Tools and Production Engineering (WZL) at Aachen University of Technology, and accuracy-related design issues have been extensively studied. Based on these investigations, strategies for kinematic calibration and error compensation have been developed.

Musculoskeletal disorders are major concern globally not just for the pain and suffering by the individual but also due to its adverse impact on the economy of the individual and the society. This results in productivity loss in both manufacturing and service sector, which has an adverse impact over the economy. The main aim of this work is to design and test an upper body exoskeleton arm that will be used for empowering the able-bodied, i.e., healthy users. The exoskeleton arm is intended to power or amplify the ability of the human elbow. Inverse dynamic model of the system is simulated through kinematic analysis and workspace analysis. The mathematical model developed by MATLAB is validated using ADAMS simulation tool. The obtained model is used to analyze the assistive torque requirements and position analysis of each task defined in the problem statement. Finally, the forward kinematic model, the inverse kinematic model, and the workspace analysis of the system are done which is universally flexible with respect to the dynamic parameters of the material used.

Chapter 3 - Description and modeling of experimental platforms

This research aims to optimize the trajectory of the foot-end in hexapod robots, with a primary focus on minimizing impact forces during ground contact and lowering overall energy consumption. By constructing both forward and inverse kinematic models, the corresponding kinematic equations for the robot’s foot-end motion were derived. These equations were employed to conduct a detailed analysis of the acceleration behaviour at the moment of touchdown. Through appropriate adjustment of trajectory equation parameters, a smoother acceleration curve during foot-ground interaction was achieved, thereby effectively suppressing impact forces. Simulation analysis confirms that the improved trajectory enhances the dynamic response of the foot-end, verifying the practicality and reliability of the proposed approach. The findings contribute valuable theoretical guidance for foot trajectory planning in hexapod robots and offer a new perspective on improving their stability and adaptability in complex terrain conditions.

A 5 degree of freedom parallel mechanism with 6 branched redundant actuators is proposed. The mechanism is composed of 4 -SPS and 2-RPS kinematic branches. The mechanism can achieve three rotational and two translational motion. The performance of the forward and inverse kinematics, singularity and workspace, is analyzed, firstly, using the vector algebra method and Newton iteration method, the forward and inverse kinematics model were obtained from numerical solution and analytic solution; on this basis, get the Jacobian matrix of mechanism, and on the basis of the three kinds of performance parameters of matrix the singularity of the mechanism was analyzed; finally with the help of Monte Carlo method, obtaining the workspace of the mechanism. The related kinematic analysis will lay a theoretical foundation for the future study of the dynamics.

A five-degree-of-freedom hybrid parallel machine tool, composed of a 3-PRS parallel robot and an X-Y series table, is designed on geometry and analyzed on kinematics. The 3-PRS parallel robot consists of three serial chains and a fixed base and a moving platform which can be moved in a pose space corresponding to the three degrees of freedom. This kind of mechanism can be applied to measuring and machining through carrying test set or cutting tool on the moving platform. Both the forward and inverse kinematics models are established based on the kinematics analysis. By means of numerical analysis, a calculation example is performed to verify the correctness of the kinematics models.Keywordskinematics analysismachine tool3-PRSparallel robot

Inverse Kinematic Model (IKM) is very crucial for real-time control of a robot for any application. Computing the IKM of continuum manipulators is a challenging task. Two types of methods exists; quantitative methods describing a model-based approach; and qualitative methods, based on learning approach. As quantitative methods are based on mathematical expression, they are more flexible for extension (increase in number of sections or collaboration between more than one manipulator). In this paper, two quantitative approaches based on Newton Raphson iterative method and Damped Least Square method, are proposed for Compact Bionic Handling Assistant (CBHA) manipulator to solve inverse kinematics directly using Forward Kinematic Model (FKM). Experimental validation is done for these methods as well as they are compared with the existing approaches named Hybrid approach and Neural Network based learning approach.

In this paper, the mechanical configuration and the principle of the measurement for a Stewart platform-based multicomponent force/torque sensor is introduced. A novel calibration method for geometric parameters is presented, which is to connect a fixed base to the top platform using one link in turn and measure the poses of the top platform. According to the poses measured on the coordinate measuring machine (CMM), the geometric parameters of the multicomponent force/torque sensor can be calculated separately. The inverse and forward kinematic model has been formulated to optimize the geometric parameters and compute the resulting forces of the multicomponent force/torque sensor. Several experiments have been carried out and the results prove that the calibration method is correct and valid

In this paper, a dual quaternion-based methodology for computing the forward and inverse kinematic models for a serial manipulator is presented. A dual quaternion-based forward kinematics model is developed for the Kuka LBR IIWA 7 R800 cobot. An inverse kinematics model is developed that uses dual quaternion differential kinematics and includes Jacobian transpose and damped least squares methods for determining Jacobian pseudo-inverse. Implementation of these methods on a given trajectory shows that, compared to damped least squares, the Jacobian transpose method is faster, but is less immune to singularity and gives more jerky motions.

A deformation model of a parallel kinematic machine tool