Six-Bar Lift

How this is calculated

A six-bar is two four-bars stacked on each other. The first carries the second, and the second keeps the end plate at a fixed angle so whatever you are carrying stays level all the way up.

It is a four-bar wearing a longer arm

Solve the linkage and the end point turns out to trace a circle about the lower ground pivot, of radius equal to both halves of the long arm added together. Not approximately — to fifteen decimal places, for every set of proportions tried, including deliberately broken ones.

That is the whole reason to build one. A four-bar that reaches twelve inches needs a twelve-inch bar, which has to fit inside the robot when folded. A six-bar reaches the same distance with two six-inch halves that fold against each other. You are buying reach per unit of folded space, and paying for it in joints, weight and things to go wrong.

What you are not buying is lifting capacity. The torque at the bottom pivot is set by the weight and how far out it sits, and a six-bar puts the weight further out.

Why this page does not use the standard formula

There is a well-known shortcut for six-bar torque: add up the link weights with a fixed set of coefficients to get one effective weight, then multiply by the arm length and the cosine of the angle. For the standard build it is exact, and this page reproduces its published figures to nine decimals.

It stops being exact as soon as you change the proportions. Lengthening only the upper half of the long arm moved the effective weight by10% across the sweep; widening the mid link's upper offset moved it by 19%. There is no single effective weight for those builds, so no single number can be right.

So the torque here comes from the linkage itself: the height of every moving piece's centre of mass is worked out at each angle, added up, and differentiated. That is exact whatever the proportions. The page then reports how far the shortcut would have been off for your build, which is the part worth knowing.

When a six-bar will not assemble

Six-bars are fussier than four-bars because both loops have to close at once. Two things go wrong:

• It cannot be built at that angle at all. The bars are not long enough to reach each other. The page says which part of the sweep is affected.
• It flips. The end plate snaps to a mirrored position partway through the travel. On paper the linkage still closes; on a robot it binds, jams, or turns itself inside out. This is flagged separately, because the numbers either side of the flip look perfectly reasonable.