Parallel Link Control for Direct Coordinate Calculation
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Solution Overview
Problem
Current link actuation devices with parallel link mechanisms require time-consuming iterative calculations using the Newton-Raphson method to determine coordinates, leading to poor accuracy in torque application and positioning, especially during high-speed multi-point movements.
Innovation Solution
A control device that calculates distal-side link center coordinates and rotation angles directly from orthogonal coordinates without approximate solutions, using normal vectors applied to plane and sphere equations, allowing for precise and efficient calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Newton-Raphson method is used to calculate coordinates of the distal-side link center, then an approximate solution can be obtained, but the calculation is time-consuming and accuracy is poor
Solution Approach 1:
The patent replaces the iterative numerical calculation method (Newton-Raphson) with a direct analytical calculation method using orthogonal coordinates. By establishing a direct mathematical relationship between the rotation angles of proximal-side shafts and the coordinates of the distal-side link center through orthogonal coordinate transformation, the system eliminates iterative approximation and achieves both high accuracy and fast calculation speed.
2Manufacturing precision
If iterative calculations are performed to obtain approximate solutions, then coordinates can be determined, but positioning accuracy and orbital accuracy are insufficient
Solution Approach 1:
The patent changes the calculation parameters from iterative approximation values to exact analytical solutions by transforming the problem into orthogonal coordinate space. This parameter transformation allows direct computation of the distal-side link center coordinates from the rotation angles, eliminating the need for iterative refinement and achieving precise positioning and orbital accuracy.
3Productivity
If the link actuation device moves through multiple points at high speed, then productivity is improved, but sufficient accuracy cannot be obtained in torque application control
Solution Approach 1:
The patent performs preliminary action by pre-establishing the exact mathematical relationship between rotation angles and distal-side coordinates through orthogonal coordinate transformation. This pre-calculated analytical model allows the system to quickly and accurately determine positioning and torque control parameters during high-speed multi-point movements, eliminating the need for time-consuming iterative calculations during actual operation.
Data Source
AI summary
A link actuation device includes: a parallel link mechanism including a proximal-side link hub, a distal-side link hub, and three or more link mechanisms coupling the distal-side link hub to the proximal-side link hub such that a posture of the distal-side link hub can be changed with respect to the proximal-side link hub; actuators for changing the posture; and a teaching unit including a conversion unit configured to calculate coordinates (Wt (=Xt, Yt, Zt)) of a distal-side link center of the distal-side link hub, which are expressed in orthogonal coordinates, from rotation angles (βn; n=1, 2, . . . ) of the end link members. A normal vector is applied to equations of a plane and of a sphere, and the equations are rearranged and used in the conversion unit.