# VectorPaint equal-pulley belts: join common tangents to outer semicircles

Language: en
Canonical: [VectorPaint equal-pulley belts: join common tangents to outer semicircles](<https://allluckly.cn/en/guides/vectorpaint-equal-pulley-belt-outline/>)
中文：[中文 HTML](<https://allluckly.cn/guides/vectorpaint-equal-pulley-belt-outline/>)
English: [English HTML](<https://allluckly.cn/en/guides/vectorpaint-equal-pulley-belt-outline/>)
Published: 2026-11-07T00:00:00+08:00
Modified: 2026-11-07T09:41:37+08:00
Author: Bison

Draw an outer belt centreline around equal, level circles, checking tangencies, straight spans and outer semicircles without mechanical-design claims.

English translation of the [Chinese original](<https://allluckly.cn/guides/vectorpaint-equal-pulley-belt-outline/>), translated on 2026-11-07. Original publication dates, attribution, code and version notes are retained.

An outer belt needs straight spans joining smoothly at tangencies, not arbitrary diagonals between circles. Construct only equal-radius, level-centred pulleys with retained sources and an outer path. This calculates no tension, friction, material thickness or real transmission ratio and assumes no automatic mechanism generator.

## Fix two equal circles at one height

Create a 1200 by 800 pixel canvas with centres (300,400)/(800,400), each radius 100. Distance 500 exceeds the radius sum 200, so circles do not intersect. Name A/B and draw a horizontal centre reference, not confusing outline with centre. These are screen coordinates, not a real machine or millimetre specification. Preserve complete circles/centres and construct the belt separately so distance edits cannot resize pulleys. Exclude crossed belts, unequal radii and tilted axes explicitly.

## Join upper/lower common tangents at extreme points

Both tops are y=300 and bottoms y=500. Draw the upper span (300,300)→(800,300) and lower (800,500)→(300,500), horizontally tangent rather than through centres. Inspect thin strokes before weight conceals errors. Vertically offset centres cannot retain these same horizontal tangents and need another construction. This is a belt centreline; stroke weight is visual, not a physical outer surface or fabrication contour.

## Join outer semicircles at all four endpoints

Follow A’s outer left semicircle from upper to lower tangent and B’s outer right semicircle from lower back to upper, completing the loop. Inner halves would cross the gap or enclose the wrong region. Use full-circle sources with verified masks or construct corresponding arcs with paths, preserving untrimmed sources without assuming a split command. Join smoothly to horizontal spans without spikes/gaps. Trace one complete loop before applying consistent stroke styling.

## Keep pulleys and belt as distinct objects

Complete circles represent pulleys; the outer loop represents the belt centreline. Contact arcs may coincide while remaining separate objects. Temporarily colour the belt to detect duplicate spans/circles. Repair fill/stacking rather than thickening a hidden belt. Optional axle circles identify centres without connecting to the belt; defer unsupported teeth/screws. This explains routing, not actual assembly or rotation speed. Define both object roles so recipients do not treat them as one cutting path.

## Change centre distance through straight-span length

Move B left by 100 in a copy, keeping level centres/radius 100, giving distance 400. Its tangent points move; outer semicircle size stays fixed and both straight spans shorten by 100. Horizontal group scaling would distort circles. This supplies no purchase length or material verification. Name 500/400 versions separately at equal scale. On restoration, check the right arc and both spans for old duplicates; ordinary objects do not follow automatically.

## Do not force this construction onto unequal or offset circles

In a rejected-control copy, shrink or raise B and inspect whether the horizontal lines still touch both circles. If tangency fails, state violated conditions instead of relabelling or shadowing gaps. You need not solve another mechanism; the comparison explains why equal radius/height were fixed. Near-looking lines are not validated tangents and decorative arrows are not motion analysis. New conditions need their own reliable geometry/requirements while this source keeps its original scope.

## Inspect closure and tangencies in the real export

Retain circles, arc sources and closed-loop version. Inspect four tangent points then the whole exported path. Heavy small-size strokes may merge belt/pulley identities; simplify separately without changing geometry. Test light/dark backgrounds; white overlays do not become openings. Name equal-level pulley schematic, dimensions and revision and exclude rejected offset tests. Explain independent arc/span dependencies for editable delivery. Readability is not mechanical acceptance.

## Check arc sources and tangent points for poor joins

For a kink, inspect attachment at the highest or lowest point and the arc-end tangent direction; do not simply add rounded corners to conceal the error. A span through a pulley may use an inner instead of outer semicircle. Distorted circles after distance editing indicate group scaling; restore circles before spans. Audit four joins instead of adding an arbitrary diagonal across a gap. Recheck equal-level circles, tangents, outer arcs and output so routing has a defined construction.

## Related tutorials and sources

[VectorPaint shape practice: build a little house from rectangles and circles](<https://allluckly.cn/en/guides/vectorpaint-basic-shapes/>), [Edit Bézier nodes in VectorPaint: smooth curves without adding anchors](<https://allluckly.cn/en/guides/vectorpaint-bezier-nodes/>).

Sources checked on November 7, 2026: VectorPaint 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store description](<https://apps.apple.com/cn/app/id1587272880>) and [Apple public version lookup](<https://itunes.apple.com/lookup?id=1587272880&country=cn>). These are exercises and checks you can perform, without a claim of step-by-step physical-device testing or verification in every target environment. Example content is instructional; follow the controls in your installed version.