Research On 3-DOF Spherical Actuator Relative Coordinate Transformation And Detection Key Technology

Three Degree of Freedom(DOF)spherical actuator has a good application prospect in space motion applications due to its multi-DOF motion characteristics.Compared to conventional 1 DOF motor,3-DOF spherical actuator’s excellent spatial kinematics brings new challenges to the classical methods such as parameter transformation,detection method and control system,etc.According to the conventional analysis of the coordinate system of the existing 3-DOF spherical actuator,it is usually assumed that the stator coordinate system and the ground coordinate system are unified,and constrained to a stationary coordinate system.This assumption has some limitations in the process of spatial motion of the 3-DOF spherical actuator.Based on the analysis and actual situation of 3 DOF spherical actuator coordinates,the coordinate transformation and position detection system of the generalized 3-DOF spherical actuator are studied.In this paper,the detection structure and methods of all kinds of 3-DOF spherical actuators at home and abroad are summarized.A new 3-DOF spherical actuator coordinate system is redefined with the facts that the stator coordinate system is separated from the ground coordinate system,and the stator(and the stator coordinate system)is defined to implement the 3-DOF motion in space.Under the new definition of coordinate system,the relative coordinate transformation method of 3-DOF spherical actuator based on quaternion method is proposed,and the comparison and analysis of conventional 3-DOF spherical actuator coordinate transformation method based on the direction cosine matrix method also illustrated in the paper.When the stator rotates in the space,the conventional coordinate transformation method of the 3-DOF spherical actuator is invalid.Otherwise,the relative coordinate transformation is still valid when the stator is stationary in the space.Some basic properties of relative coordinate transformations are analyzed and verified in the paper.Based on the basic idea of relative coordinate transformation,the rotor detection and transmission module and the stator detection and fusion module are respectively designed to be installed on the rotation and stator sphere of a 3-DOF spherical actuator.The rotor detection and transmission module realizes rotor attitude detection and sends it out through the Zigbee communication module.The stator detection fusion module realizes the stator attitude detection,accepts the attitude data from the rotor,sends the data to the upper computer for the calculation of relative coordinate transformation,and completes the corresponding software and hardware design.The relative coordinate transformation algorithm based on quaternion was programmed in MATLAB.With the help of Labview software,the data transferred from the lower computer are read and preprocessed.Then the relative coordinate transformation and the position of specific points of rotation and stator are realized by embedding MATLAB script,and the 3-DOF spherical actuator relative position detection system is constructed.The relative coordinate transformation of the rotor attitude data obtained from sensor detection is used to programed in MATLAB.The compared results verifies the correctness of the relative coordinate transformation.Based on the joint debugging of software and hardware of the detection system,the transformed results can be displayed intuitively in the interface of the host computer.The experimental results verify that the relative coordinate transformation algorithm of the 3-DOF spherical actuator,in which the conventional coordinate transformation algorithm is the special case of the relative coordinate transformation,can be effectively applied to the motion of the 3-DOF spherical actuator.