Five-axis trajectory generation considering synchronisation and nonlinear interpolation errors

This paper presents a novel real-time interpolation technique for 5-axis machine tools to attain higher speedand accuracy. To realize computationally efficient real-time interpolation of 6DOF tool motion, a joint workpiece-machine coordinate system interpolation scheme is proposed. Cartesian motion of the tool centre point (TCP) isinterpolated in the workpiece coordinate system (WCS), whereas tool orientation is interpolated in the machinecoordinate system (MCS) based on the finite impulse response (FIR) filtering. Such approach provides several ad-vantages: i) it eliminates the need for complex real-time spherical interpolation techniques, ii) facilitates efficientuse of slower rotary drive kinematics to compensate for the dynamic mismatch between Cartesian and rotary axesand achieve higher tool acceleration, iii) mitigates feed fluctuations while interpolating near kinematic singulari-ties. To take advantage of such benefits and realize accurate joint WCS-MCS interpolation scheme, tool orientationinterpolation errors are analysed. A novel approach is developed to adaptively discretize long linear tool movesand confine interpolation errors within user set tolerances. Synchronization errors between TCP and tool orienta-tion are also characterized, and peak synchronization error level is determined to guide the interpolation parameterselection. Finally, blending errors during non-stop continuous interpolation of linear toolpaths are modelled andconfined. Advantages of the proposed interpolation scheme are demonstrated through simulation studies and vali-dated experimentally. Overall, proposed technique can improve cycle times up to 10% while providing smooth and accurate non-stop real-time interpolation of tool motion in 5-axis machining.

High-precision modeling of CNCs’ spatial errors based on screw theory

A method for establishing machine tool’s spatial error model is put forward based on screw theory, which is different from the traditional error modeling method. By analyzing the position relationship between the ideal coordinate vector and the actual coordinate vector jointly affected by linear errors and angular errors, a single-axis screw conversion matrix error expression is brought up based on screw theory. Meanwhile, the comprehensive spatial error model of the CNC machine tool is derived by considering the influence of the workpiece motion chain and the tool motion chain on the model. Further, to compensating spatial errors of CNCs, such screw theory-based model is embedded in the error compensation system by means of integration of a few specific application examples. And in order to evaluate the compensation effects, an integrated evaluation method of quantitative spatial diagonal calculation and MATLAB simulation is proposed. Application results show that the screw theory-based spatial error model of tool has a very substantial compensation effect, which makes the position error of the machine tool decreased by about 80%.

Kinematic Analysis and Parameter Measurement for Multi-Axis Laser Engraving Machine Tools

Multi-axis Laser Engraving Machine Tools (LEMT) are widely used in precision processing of parts with complex surface. The accuracy of kinematic model and parameter measurement are the key factors determining the processing quality of LEMT. In this paper, a kinematic model of multi-axis LEMT was established based on Homogeneous Transformation Matrix (HTM). Two types of unknown parameters, linkage parameters and positioning parameters, were measured in the presented model. Taking advantage of the characteristics of laser processing, this paper proposed a rapid measurement method of linkage parameters by combining the machine tool motion with the laser marking action. For positioning parameters, this study proposed a non-contact measurement method based on structured light scanner, which can obtain the translation values and the rotation values from the Workpiece Coordinate System (WCS) to the Basic Coordinate System (BCS) simultaneously. After the measurement of two kinds of parameters of a multi-axis LEMT was completed, the processing of a spatial curve was performed and the average contour error was controlled at 15.1 µm, which is sufficient to meet the project requirements.

Kinematic Tool-Path Smoothing for 6-Axis Industrial Machining Robots

The demands for machining by industrial robots have been increasing owing to their low installation cost and high flexibility. A novel trajectory generation algorithm for high-speed and high-accuracy machining by industrial robots is proposed in this paper. Linear interpolation in the workspace and smooth trajectory generation at the corners are important in industrial machining robots. Because industrial robots are composed of rotational joints, the joint space has a nonlinear relationship with the workspace. Therefore, linear interpolation in the joint space, which has been widely used in conventional machine tools, does not guarantee linear interpolation in the actual machining workspace. This results in the degradation of the machining surface. The proposed trajectory generation algorithm based on the decoupled approach can achieve linear interpolation in the workspace by separating the position commands into Cartesian coordinates and the orientation commands into spherical coordinates. In addition, a novel corner smoothing method that generates a smooth and continuous trajectory from discrete commands is proposed in this paper. The proposed kinematic local corner smoothing generates a smooth trajectory by using a 3-segmented constant jerk profile at the corners in the joint space. The sharp corners can thereby be replaced by smooth curves. The resulting cornering error is controlled by varying the cornering duration. The simulation results demonstrate the effectiveness of the proposed kinematic smoothing algorithm in achieving linear tool motion in straight sections and in generating smooth trajectories at corner sections within the user-defined tolerance.

Digital image processing to detect subtle motion in stony coral

Coral reef ecosystems support significant biological activities and harbor huge diversity, but they are facing a severe crisis driven by anthropogenic activities and climate change. An important behavioral trait of the coral holobiont is coral motion, which may play an essential role in feeding, competition, reproduction, and thus survival and fitness. Therefore, characterizing coral behavior through motion analysis will aid our understanding of basic biological and physical coral functions. However, tissue motion in the stony scleractinian corals that contribute most to coral reef construction are subtle and may be imperceptible to both the human eye and commonly used imaging techniques. Here we propose and apply a systematic approach to quantify and visualize subtle coral motion across a series of light and dark cycles in the scleractinian coral Montipora capricornis. We use digital image correlation and optical flow techniques to quantify and characterize minute coral motions under different light conditions. In addition, as a visualization tool, motion magnification algorithm magnifies coral motions in different frequencies, which explicitly displays the distinctive dynamic modes of coral movement. Specifically, our assessment of displacement, strain, optical flow, and mode shape quantify coral motion under different light conditions, and they all show that M. capricornis exhibits more active motions at night compared to day. Our approach provides an unprecedented insight into micro-scale coral movement and behavior through macro-scale digital imaging, thus offering a useful empirical toolset for the coral research community.

Directing the Material Flow and Form Filling through a Multi-axis Forming Process

Multi-axis forming is a six degree of freedom forming process. This process influences actively the material flow by defining a six dimensional tool motion path and the corresponding tool velocity. Within this process, it is possible to combine a linear forming movement followed by a rolling movement and therefore tailor the induced local material properties of the work piece. The research objective of this work is to observe and quantify the interaction between tool motion and material flow for the purpose of process planning. Experiments are conducted to examine the horizontal material flow within a multi-axis forming process of a plane L-shaped work piece. Three different punches form the material: Flat, cylindrical and cone-shaped. The horizontal material flow is recorded through a transparent die by a camera to measure the material flow for different tool motions. It is shown, that a multi-axis forming process can adjust the local material flow. The resulting redirection of the material flow after the sharp inward facing edge of the L-shape is analyzed and compared. With a smaller active zone compared to a standard linear pressing, the multi-axis forming forces are reduced. In addition, the reservoir with the remaining material is more concentrated. Finally, it is possible to direct the material flow with the punch motion, which can be used to determine local part properties.