Papers by Keyword: Homogeneous Transformation

Abstract: Various environmental factors will adversely influence accelerometers working in the field. Mixed inputs, including external causes and the intended acceleration, are important contributors to the problem. As a consequence, calibrating accelerometers with multiple accelerations is required by manufacturers and customers. We introduce a multi-component mechanical system called vibrafuge to provide multiple accelerations. In this paper, we deduce a general model of the accelerations reproduced by an ideal vibrafuge with homogeneous transformation of matrix. Based on the model, we have an elementary analysis of the components of the output acceleration and point out two byproducts. Investigation in this paper could lay the groundwork for vibrafuge testing of accelerometers.

Abstract: The ball-end cutter plays an important role in machining free-form surfaces due to its adaptability to a surface. It is widely used in aerospace, automobile, and die/mode industries. Thus, the demand for higher cutting performance and lower cost of the ball-end cutter has been increasingly focused. In this paper, based on normal helix cutting edge geometric model, the cone wheel, which was used to grind the rake and flank face of ball-end cutter, was designed. Then, we use homogenous coordinate transformation to derive for the ball-end cutter and establish the mathematical model for grinding this type cutter in terms of grinding parameters. Finally, the cutting angles of ball-end cutter were discussed.

Abstract: In this paper, a novel approach of linear octree is employed to represent discrete tools and build their swept volumes along machining trajectories. Firstly, a data structure of linear octree is defined as the base of geometrical transformations. The linear octree can be extended into leaf nodes in the deepest level for simplifying homogeneous transformations, and all leaf nodes in the deepest level can also be concentrated into a linear octree for saving storage capacity inversely. Secondly, tool trajectories are interpolated as short lines, and swept volumes between neighbor interpolation points are defined as the Minkowski sum of their cell sets at both locations. Thirdly, equations of the rotation matrix for local coordinate system, roll, pitch and yaw angles of tool orientations are established to define the global rotation motions. Finally, a case of discrete sphere tool and its swept volume modeling are studied to validate the proposed approach.

Abstract: Five-axis CNC machine tool is the top product of numerically controlled machine tool. Kinmatic accuracy is an important index to evaluate the quality of mechanism. Kinematic accuracy analysis of the Five-axis machine tool in previous study ignores the randomness of each input error component, so the conclusions are imprecise. Using the homogeneous transformation, inverse kinematics of VMC650 Five-axis machine tool is calculated. Based on Multi-body System Theory, error model of the machine tool is presented. Considering the randomness of every input error components, applying the Monte Carlo method, math model of kinematic reliability of the mechanism is deduced. The calculation method of kinematics reliability are put forward applying point evaluation and track evaluation. Kinematic reliability analysis provides some theoretical reference for improving the machining accuracy and operation life of machine tool.

Abstract: The space relationships among flange coordinate, camera coordinate and calibration reference coordinate are analyzed. A simple calibration method for the relationship of the eye-in-hand of robot vision is proposed and corresponding experiment system is designed. The result of experiments shows that this method can work simple and shortcut with higher precision.