Spherical Parallel Link Control for Real-Time Forward Kinematics
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Solution Overview
Problem
Existing link actuation apparatuses face challenges in achieving accurate positioning and real-time forward transformation due to calculation errors and time-consuming convolution operations, making real-time processing and long-distance movement from an unknown state difficult.
Innovation Solution
A link actuation apparatus with a spherical drive mechanism, featuring a first and second link hub connected by at least three link mechanisms, where each mechanism includes rotatable link members and a central link member, utilizing spherical trigonometry to calculate the position and attitude of the second link hub from angles of the first end link members, enabling real-time forward transformation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If forward transformation is performed using convolution operations with repetitive calculations, then an approximate solution can be obtained, but calculation time increases significantly making real-time processing difficult
Solution Approach 1:
The patent replaces the mechanical convolution operation system with a spherical trigonometry calculation system. By using spherical trigonometric relationships directly to calculate tip end position from drive source angles, the system eliminates the need for repetitive convolution operations, achieving both real-time processing capability and accurate positioning without the time-consuming iterative calculations of traditional methods
Solution Approach 2:
The patent changes the calculation parameters from using convolution operations with multiple sums of products to using spherical trigonometry formulas. This parameter change transforms the computational approach from iterative approximation to direct calculation, reducing computation time while maintaining positioning accuracy
2Ease of operation
If a large number of sums of product of trigonometric functions and inverse trigonometric functions are used in theoretical equations, then forward transformation can be performed, but calculation errors accumulate
Solution Approach 1:
The patent substitutes the complex mechanical calculation system involving multiple trigonometric and inverse trigonometric functions with a spherical trigonometry system. This replacement reduces the number of calculation steps and eliminates the accumulation of calculation errors while maintaining the forward transformation capability to calculate tip end position from drive source angles
3Productivity
If real-time processing is not achieved due to time-consuming calculations, then direct teaching or operation from unknown state becomes impossible, but using approximate methods reduces positioning accuracy
Solution Approach 1:
The patent replaces the time-consuming convolution calculation system with spherical trigonometry calculations that can be performed in real-time. This substitution enables direct teaching and operation from unknown states while maintaining high positioning accuracy, as the spherical trigonometry formulas provide exact solutions without the approximations required by convolution methods
Data Source
AI summary
A link actuation apparatus that actuates a parallel link mechanism where a spherical drive mechanism is constructed includes a controller configured to calculate, based on spherical trigonometry, an attitude of a second link hub from angles βA1 and βA2 that represent the attitude of a first end link member with respect to a first link hub in two of at least three link mechanisms. The link actuation apparatus capable of performing forward transformation in real time is thus provided.