Chains require slack. If the chain is tight at any point in the suspension travel, then it is not slack enough. Tension shouldn't even be in the chain vocabulary.
Unless you a have a fancy offroad bike that has the drive sprocket on the same axle as the swingarm, the chain slack will change as the suspension moves up and down. It usually gets tighter as the suspension is in jounce and slacker as the suspension rebounds.
Step one is to make it possible to align all 3 of these in a straight line:
1. Front sprocket rotational centre
2. Swingarm pivot dead centre
3. Rear axle rotational center
When everything is in a straight line, then the chain is at its point of minimum slack. This is where you follow the diagram on the box the chain came in and set the slack to that ¼" or whatever it says
While it’s true aligning the 3 axle points is the least slack, there is no guarantee this is the standard position of the bike at rest. The unloaded bike with both wheels on the ground is the correct way to measure and set slack.
Manufacturers have taken into consideration the chains length with wheels on the ground and supply slack specs based on that.
The bike I ride is notorious for looking like the chain is about to fall off, but when the suspension is compressed enough to line up the 3 axes, the slack disappears. If I set the chain with not enough slack, the suspension will bind up before the spring and shock can do its job. It's literally using the output shaft and the chain as a travel limiting strap.
If you don't have enough slack, you can damage countershaft seals, bearings, the output shaft splines. This damage takes a long time to cause a problem somost people don't make the connection.
Some bike designs might make it impossible to line up all three... I don't know. That's how it's been for all the bikes I've owned and worked on.
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