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	<id>https://apm.bplaced.net/w/index.php?action=history&amp;feed=atom&amp;title=Whippletree</id>
	<title>Whippletree - Revision history</title>
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	<updated>2026-08-14T02:17:25Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20502&amp;oldid=prev</id>
		<title>Apm: /* ZigZag differentials */</title>
		<link rel="alternate" type="text/html" href="https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20502&amp;oldid=prev"/>
		<updated>2026-07-09T13:03:20Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;ZigZag differentials&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 15:03, 9 July 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot;&gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The concept can be generalized.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The concept can be generalized.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== ZigZag differentials ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;ZigZag differentials&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{wikitodo|Maybe give this topic its own dedicated page.}} &amp;lt;br&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{wikitodo|Maybe give this topic its own dedicated page.}} &amp;lt;br&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Apm</name></author>
	</entry>
	<entry>
		<id>https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20484&amp;oldid=prev</id>
		<title>Apm: /* Use cases */</title>
		<link rel="alternate" type="text/html" href="https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20484&amp;oldid=prev"/>
		<updated>2026-07-09T12:13:13Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Use cases&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:13, 9 July 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l48&quot;&gt;Line 48:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 48:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;That has a pole in lever ration for the square wave geometry. &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;That has a pole in lever ration for the square wave geometry. &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Used in reverse that can be used for tensioning [[ReChain core &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;chains&lt;/del&gt;]] &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Used in reverse that can be used for tensioning [[ReChain core &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;chain&lt;/ins&gt;]]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s &lt;/ins&gt;&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Actually there wan would want jut one trapezoidal &amp;quot;zig&amp;quot; in the chain. &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Actually there wan would want jut one trapezoidal &amp;quot;zig&amp;quot; in the chain. &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;And friction might be a concerns (see below). &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;And friction might be a concerns (see below). &amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Apm</name></author>
	</entry>
	<entry>
		<id>https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20483&amp;oldid=prev</id>
		<title>Apm: basic page</title>
		<link rel="alternate" type="text/html" href="https://apm.bplaced.net/w/index.php?title=Whippletree&amp;diff=20483&amp;oldid=prev"/>
		<updated>2026-07-09T12:12:49Z</updated>

		<summary type="html">&lt;p&gt;basic page&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{stub}}&lt;br /&gt;
&lt;br /&gt;
These mechanisms are in effect acting like mechanical differentials. &amp;lt;br&amp;gt;&lt;br /&gt;
Just for non-circular reciprocative motion. Roughly linear acting for small motions. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A whippletree acts like a binary tree (a the name suggests) &amp;lt;br&amp;gt;&lt;br /&gt;
with an power or two exponentially increasing number of branches. &amp;lt;nr&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The concept can be generalized.&lt;br /&gt;
&lt;br /&gt;
== ZigZag differentials ==&lt;br /&gt;
&lt;br /&gt;
{{wikitodo|Maybe give this topic its own dedicated page.}} &amp;lt;br&amp;gt; &lt;br /&gt;
{{wikitodo|This needs image illustration(s).}} &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One gets to &amp;quot;zigzag differentials&amp;quot; by … &amp;lt;br&amp;gt;&lt;br /&gt;
★ distorting the shape and &amp;lt;br&amp;gt;&lt;br /&gt;
★ changing the topology &amp;lt;br&amp;gt;&lt;br /&gt;
… of a [[whippletee]] mechanism &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;quot;zigzag differentials&amp;quot; seem to be a more generally useful mechanism than whippletrees. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
By making the system asymmetric and continuing always on one side &amp;lt;br&amp;gt;&lt;br /&gt;
one gets a linear increase in force distributing outward ending branches. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
To not go diagonal one can alternate the direction. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One basically gets a square wave zig-zag chain with overstands &amp;lt;br&amp;gt;&lt;br /&gt;
and trying to pulling it straight distributes the force &amp;lt;be&amp;gt;&lt;br /&gt;
to all &amp;quot;zigs&amp;quot; on one side and &amp;lt;br&amp;gt;&lt;br /&gt;
to all &amp;quot;zags&amp;quot; on the other side. &amp;lt;br&amp;gt;&lt;br /&gt;
The force distributing outputs are clamp-together or push-apart lever-pairs all along the chain. &amp;lt;br&amp;gt;&lt;br /&gt;
All these pairs need to be connected to a load to not &amp;quot;free-wheel&amp;quot; collapse. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Complicatingly the axial position changes a bit due to the chain stretching a bit  &amp;lt;br&amp;gt;&lt;br /&gt;
when tensioned and distributing the load that also may suquiush/stretch a bit. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One can obviously pick various lever ratios.&lt;br /&gt;
&lt;br /&gt;
=== Use cases ===&lt;br /&gt;
&lt;br /&gt;
This can be used to …&lt;br /&gt;
* Clamp several things sideways too [[ReChain strut]] co-using the same internal [[ReChain core chain]] tension&lt;br /&gt;
* Clamp [[ReChain strut]] together sideways (Particularly with [[Fir tree joint]]s)&lt;br /&gt;
&lt;br /&gt;
Instead of clamping or spreading with the overstands one can &amp;lt;br&amp;gt;&lt;br /&gt;
tap the output on the chain coaxial linking segment. &amp;lt;br&amp;gt;&lt;br /&gt;
That has a pole in lever ration for the square wave geometry. &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Used in reverse that can be used for tensioning [[ReChain core chains]] &amp;lt;br&amp;gt;&lt;br /&gt;
Actually there wan would want jut one trapezoidal &amp;quot;zig&amp;quot; in the chain. &amp;lt;br&amp;gt;&lt;br /&gt;
And friction might be a concerns (see below). &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Friction limiting  ===&lt;br /&gt;
&lt;br /&gt;
If the force comes from the side of the zigs and zags &amp;lt;br&amp;gt;&lt;br /&gt;
rather than from pulling on the zigzag chain &amp;lt;br&amp;gt;&lt;br /&gt;
then a concern is friction adding up to the point of self-locking. &amp;lt;br&amp;gt;&lt;br /&gt;
Especially for macroscale (and [[scale transposed prototyping]]). &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Related ==&lt;br /&gt;
&lt;br /&gt;
* [[RepRec]]&lt;br /&gt;
* [[Suitable mechanisms]]&lt;br /&gt;
* [[ReChain electrical diode analogy]]&lt;br /&gt;
* [[Why diodes in parallel are problematic]] &amp;lt;br&amp;gt;{{wikitodo|An image illustrating the mechanical problem would be helpful.}}&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
&lt;br /&gt;
* https://en.wikipedia.org/wiki/Whippletree_(mechanism)&lt;br /&gt;
&lt;br /&gt;
== Misc ==&lt;br /&gt;
&lt;br /&gt;
It is whipple not whiffle. &amp;lt;br&amp;gt;&lt;br /&gt;
There are whiffle-shields which are an entirely different idea.&lt;/div&gt;</summary>
		<author><name>Apm</name></author>
	</entry>
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