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Motion in 3-D: Newport Hexapod Coordinate Systems

Motion in 3-D: Newport Hexapod Coordinate Systems
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Motion in 3-D: Newport Hexapod Coordinate Systems - 1

TECHNICAL NOTE Motion in 3-D: Newport Hexapod Coordinate Systems Controlling Motion in 3-D space requires a user to have a clear understanding of the relationship between end effector positions and positions of devices under test. Regardless of whether it is an industrial positioning platform used in machinery, using a cutting tool and a work piece, or an electro-optical beam steering setup for advanced research in a diffractometry using a laser beam and a sample, precise readings and controls of both end effectors and devices are of key importance. Due to the complexity of motion in 3-D, multi-axis systems can present many issues without careful design and considerations. Newport Hexapods provide innovative user-definable coordinate systems to answer this challenge, leading the way of user-friendly multi-axis positioning platforms available on the market. This tech note illustrates the three user-definable coordinate systems and helps with integration and configuration of the Hexapods in experimental setups or manufacturing process, thus to help maximize the benefits of using the line of Newport’s Hexapod products. To uniquely represent the position of a moving platform in three-dimensional space, one must specify its spatial location and angular orientation with three linear and three rotational coordinate values. The Newport HXP series of Hexapods uses a Cartesian coordinate system for translation and the Bryant angles for rotation, which are frequently used in robotics and aviation. (See Figure 1) A position (X Y Z U V W) represents a XYZ location of the center point of the platform in a 3-D space in right-handed Cartesian coordinate system as well as orientation in roll, pitch and yaw (U V W, TaitBryan angles definition). Figure 1: Setup Configuration for Optical Quality Testing with Gimbal To understand how the position (X Y Z U V W) is reached in the Hexapod coordinate systems, consider a move defined by position (X Y Z U V W) starting from the position (0 0 0 0 0 0). The Tool coordinate system is set to the position (X Y Z) in the Work coordinate system. Then, it rotates about the z axis of the Tool coordinate system (W), rotates about the new y axis of the Tool coordinate system (V) and rotates about the new x axis of the Tool coordinate system (U). All rotations are made clockwise for positive rotations. When positioning commands are given in Cartesian coordinates and Bryant angles, they are transformed by the Newport HXP controller to the specific positions and velocities for each of the six Hexapod actuators before execution. All individual positions for the six actuators are taken as a set to define a unique position (location and orientation) of the Hexapod in the coordinate system. The transformation of coordinate to the actuator lengths is fully transparent. Understanding the Tool, Work and Base coordinate systems How does the Hexapod uniquely determine the position (location and orientation in X Y Z U V W)? As we are familiar with scalar fields in mathematics, a point is a sufficient geometric element to specify spatial positions (X Y Z) in a 3-D space. However, this representation is insufficient to identify directions associated with angular positions (U V W). It is however

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Motion in 3-D: Newport Hexapod Coordinate Systems - 2

TECHNICAL NOTE Motion in 3-D: Newport Hexapod Coordinate Systems 0), the upper surface of the top plate is close to mid travel for the HXP50 and the HXP1000, and it is close to the lower extreme position for the HXP100); 3) The XY plane of the coordinate system is parallel to the base plate; 4) The W-axis (Yaw orientation) matches the orientation defined in the Hexapod drawing. (The motor cables point in the positive X-axis direction of the World coordinate system.) The World Coordinate System is an absolute fixed reference to the outside world. It is defined such that, in the default...

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TECHNICAL NOTE Motion in 3-D: Newport Hexapod Coordinate Systems Why is the Base coordinate system defined relative to the World coordinate system, instead of the Work coordinate system? By referencing the World coordinate system, it is possible to take into account any change in the position of the Hexapod without affecting the motion commands of the Tool in the Work coordinate system. A good example is a Hexapod mounted on a moving platform at the center of a multi-axis goniometer in a diffractometry application. (Figure 4) When the Hexapod itself is rotated or moved to a different...

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Motion in 3-D: Newport Hexapod Coordinate Systems axes relative to the beam from the starting position, allowing the material processing on the surface of the sample, as an example. This two pivot concept also applies to the inspection, metrology or traditional machining processes. Typical applications for the Hexapod include optical alignment and calibration, biomedical engineering and surgical robotics, satellite and telescope positioning, sensor metrology and calibration, and semiconductor test and metrology. For additional information, please visit the Newport HXP series Hexapod webpage...

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