3D Turn Trajectory in Motion Guides for Tangent-Continuous Rolling
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Solution Overview
Problem
The existing motion guide apparatuses face issues with three-dimensional complex turn portions, where the tangent lines to the turn portion trajectories are not continuous with the straight trajectories of the rolling path and return portion, leading to deteriorated movement, reduced durability, and noise generation.
Innovation Solution
The motion guide apparatus incorporates a rail member and a block with rolling elements, where the three-dimensional trajectory of the turn portion is formed based on a cross-sectional trajectory curve in the X-Z cross section and a longitudinal trajectory curve on a virtual plane, ensuring that the X and Z coordinates of the turn portion align with the cross-sectional curve, and the Y-coordinate aligns with the longitudinal curve, allowing for continuous tangent lines with the rolling path and return portion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a three-dimensional trajectory is formed by superimposing two swept curved surfaces, then the turn portion can accommodate complex spatial constraints, but the tangent lines become discontinuous with the rolling path and return portion
Solution Approach 1:
The patent transitions from conventional two-dimensional trajectory design to three-dimensional trajectory design by utilizing swept curved surfaces in spatial dimensions. The first swept curved surface is generated by sweeping a cross-sectional trajectory curve along the longitudinal direction, and the second swept curved surface is generated by sweeping a longitudinal trajectory curve along the lateral direction. The intersection of these two three-dimensional surfaces defines the turn portion trajectory, enabling accommodation of complex spatial constraints while maintaining tangent line continuity through proper mathematical formulation of the trajectory parameters.
2Reliability
If the turn portion follows a simple arc trajectory, then the tangent line continuity is maintained, but the ability to accommodate complex spatial constraints is limited
Solution Approach 1:
The patent extends the trajectory design from two-dimensional arc trajectories to three-dimensional swept curved surfaces. By defining the turn portion as the intersection of two three-dimensional surfaces (first swept curved surface and second swept curved surface), the design gains additional degrees of freedom to accommodate complex spatial constraints while maintaining the mathematical continuity required for tangent line smoothness.
Solution Approach 2:
The patent employs parametric equations to define the trajectories, allowing continuous adjustment of trajectory parameters such as curvature radius, sweep distance, and intersection angles. This parametric approach enables optimization of both the tangent line continuity (through derivative continuity) and the adaptability to spatial constraints (through parameter tuning), resolving the contradiction between reliability and versatility.
Data Source
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AI summary
A motion guide apparatus is provided in which even if at least part of a turn portion is a three-dimensional trajectory that is three-dimensional and complex, it is possible to approach at least one of a rolling path and a return portion substantially along a tangent line. At least part of the three-dimensional trajectory of the turn portion is formed on the basis of a cross-sectional trajectory curve (14) in an X-Z cross section of the motion guide apparatus, and a longitudinal trajectory curve (15) drawn on a virtual plane VP where a longitudinal direction of the motion guide apparatus is a Y-axis, and a trajectory length ω from a turn start point A of the cross-sectional trajectory curve (14) is a length ω of a W-axis. X and Z coordinates of the three-dimensional trajectory are X and Z coordinates of the cross-sectional trajectory curve (14). A Y-coordinate of the three-dimensional trajectory is a Y-coordinate of the longitudinal trajectory curve (15) where the ω of the W-axis of the virtual plane VP is a variable.