Where a joint stops working when its dimensions change

When a dimension is moved on this site, a formula first checks whether the combination of dimensions satisfies the conditions of that joint, and only when it does is the shape rebuilt and inspected. For dimensions that fail, the site shows "These dimensions do not work" and states the condition that was hit in a sentence. Meanwhile the screen keeps the shape from the last valid dimensions ("Showing the shape from the last valid dimensions"). This article covers what the judgment checks, and the key features of the form that can be read from the dimensions that tend to hit it. The judgment is a check on the 3D shape, and it does not examine the strength of a real joint.

What the judgment checks: the shape only

Four checks are common to every joint: the pieces do not overlap, the volumes of the pieces add up, each piece is a single solid, and the dimensions have been made as specified. For joints that have an assembly sequence, the site also checks whether the pieces can be moved in that sequence and taken apart.

The conditions of each joint are written for combinations of dimensions, in the form "keep this difference" or "keep this much wood". The lower-limit values are guideline values set by the site and are not figures found in published references, so this article does not give them.

Ari (dovetail): the difference between head and neck

The first condition that appears for the ari-tsugi (dovetail scarf joint) and the ari-kake is that the head must be sufficiently wider than the neck. If the head is no wider than the neck, the dovetail is just a rectangular projection and pulls straight out.

A real dovetail also widens toward its tip, like the tail of a dove^[2][3]. Making the projection in an inverted V shape is said to make the piece hard to pull out^[1]. The key of the dovetail is therefore the difference between the width of the neck and the width of the head.

At the same time, the wider the head, the less wood remains on both sides of the dovetail socket. The site places a condition on the wood beside the socket to judge this limit. Separately, there is a condition that the neck width be kept at the lower end of the dovetail as well, and it is hit when the neck is made thinner or the slope larger. For the gooseneck joint, a further condition applies: the tip of the head must be sufficiently wider than the neck, or it does not take the form of a gooseneck.

Peg and mechigai: shifting to release

In the kanawa-tsugi (rabbeted scarf splice with a square peg) and the shiribasami-tsugi (rabbeted scarf splice with a hidden mechigai and a square peg), the length of the mechigai (a small locating tongue) must be shorter than the width of the komisen (a square peg). After the peg is pulled out, shifting the upper piece along the length of the member by the width of the peg frees the mechigai from the mortise of the other piece. This condition is checked before the shape is built, and dimensions that do not satisfy it are judged "These dimensions do not work".

In a real kanawa-tsugi, too, the joint cannot be dropped in from above because of the T-shaped mechigai at the end of the gooseneck^[4][5]. Araki Komuten's explanation says that after assembly the pieces are shifted along the axis by the amount of the peg^[4]. The site judges the relation between the width of the peg and the length of the mechigai as the condition for whether the pieces can be released with the peg removed.

In the shiribasami-tsugi, the mechigai is placed only in the middle of the width and height of the member and hidden inside it. A condition is therefore added to keep wood above, below and on both sides of the mechigai. An explanation based on material supervised by Yamabe says that the shiribasami-tsugi differs from the kanawa-tsugi only in how the mechigai is combined, and that it is superior in design because no mechigai appears on the side faces^[6].

Okkake-daisen-tsugi: ago and mechigai

For the okkake-daisen-tsugi (sloped scarf splice with square pegs) there is a condition that the upper piece must remain outside the mechigai of the lower piece. The more the okkake (the sloped faces) change or the thicker the mechigai is made, and the smaller the step of the ago (jaw), the less wood of the upper piece remains outside the mechigai.

In real joints, too, the structural features of the okkake-tsugi are said to lie in the ago and in the bearing stress along the grain at the joint. The report discusses that widening the ago increases the bearing area, but making it too large reduces the width left at the center of the joint^[7]. The site's check likewise judges the relation that moving one dimension changes how much wood remains elsewhere. However, what it examines is whether the wood remains, and it does not calculate bearing stress as the report does.

Wood left beside a hole

The conditions of joints and shiguchi that have holes, such as tenon mortises, peg holes, dovetail sockets, gooseneck sockets and sao slots (a sao is a long, slender tenon), include conditions that keep wood around the hole, because the more holes and steps are cut, the less wood remains around them. The condition text gives the reason for keeping the wood; for the naga-hozo sashi hanasen-uchi (through tenon locked with a hanasen, a slender, slightly tapered peg), for example, it is so that the tip of the tenon does not split and let the tenon come out.

Valid and strong are different things

What the site judges is whether the shape holds: overlap, connectedness and whether the pieces can be removed. Valid dimensions do not show that the real joint is strong at those dimensions. The relation between dimensions and strength of real joints is a question handled by experiments and design formulas; for the okkake-tsugi, for example, four-point bending tests have examined how rotational stiffness changes with member depth and ago width^[7]. This article does not go into that question of strength.

See them in 3D

• Neck and head of a dovetail: Ari-tsugi, Koshikake-ari-tsugi
• Peg and mechigai: Kanawa-tsugi, Shiribasami-tsugi
• Ago and mechigai: Okkake-daisen-tsugi
• All joints