A parallelogram linkage can move a connecting bar while keeping that bar facing the same direction. Its two cranks have equal pivot radii, and the distance between their fixed shafts matches the distance between the connecting bar’s end joints. The bar stays parallel to the fixed shaft line. Its ends still follow circular arcs: keeping direction does not mean travelling along a straight line.
Build a bar that keeps its heading
The new Parallel Motion Bench makes that distinction visible from above. A yellow crank and a red crank turn on separate retained vertical shafts. Each crank uses a seven-hole beam attached to a keyed mounting hub by two separated pins. A blue five-hole bar connects the same-side outer ends through two retained joint axles. The gears underneath are mounting hubs; they do not mesh or transmit motion to one another.
The fixed shafts stand four hole spacings apart. The blue bar’s first and fifth holes are also four spacings apart. Each crank’s middle-to-end distance is three spacings. At eight millimetres per spacing, those dimensions are thirty-two millimetres between the shafts and twenty-four millimetres from each shaft to its outer joint. Count gaps between hole centres, not the number of holes or the plastic’s outside length.
Bricks Master Builders’ credited demonstration shows a parallel linkage on a motorized wheeled assembly. It inspired the question about keeping a bar’s direction. Our horizontal, hand-operated bench has its own dimensions, retained joints and step sequence. It does not recreate that vehicle, its motor drive or its hidden construction. The short source clip includes some fitting and operation, but does not supply the complete inventory and full assembly sequence used by our guide.
Predict direction and path separately
Imagine drawing an arrow along the blue bar. As you rock the yellow crank, will that arrow turn with it? Now imagine tracing one end of the bar. Will its trace be straight? Make both predictions before moving the control below.
Interactive: Can a bar keep its direction on a curved path?. Predict heading and endpoint path, scrub a limited-angle parallelogram, compare its arcs with a straight reference, vary virtual radius and reset. Ideal rigid links, not measured accuracy.
In the ideal geometry, both crank tips receive the same displacement. The difference between the tips therefore stays equal to the fixed shaft spacing. That is why the bar keeps its heading. Every point on the bar moves by the same amount, a motion called translation. Translation can follow a curve; it does not require a straight sliding guide.
The dashed line in the diagram is a straight reference through the initial endpoint positions. It is not a physical rail in the build. At the native twenty-four-millimetre crank radius and thirty degrees from the perpendicular starting direction, the endpoint shifts twelve millimetres along the fixed shaft line. It also comes inward by about three point two millimetres from that straight reference. The heading stays unchanged in the ideal model even though the path bows away from the line.
These are calculated pin-centre positions, not measurements of manufactured beams. Real holes have clearance, beams can flex, and rubbing can make the motion uneven. The lab’s alternative radii are virtual thought experiments. Changing a real crank length needs another support and clearance review; the existing guide validates only its stated configuration and limited range.
Make a fair direction-versus-path observation
Assemble the free guide and check the two hub pins on each crank. Check the stops above and below both main bearings and both connecting joints. Keep the frame flat on a level table and hold only that stationary frame. Gently rock one crank by no more than thirty degrees either side of the starting position. The linkage carries the other crank; do not push it along a different path.
Place paper beside the frame, clear of every moving part. Sketch the fixed shaft line and compare it with the blue bar at several positions. Observe from directly above to reduce perspective error. A photograph you take yourself can help compare positions, but you do not need to upload anything. Keep the camera position, assembly and chosen joint holes the same between trials.
| Crank setting | Bar parallel to fixed line? | Endpoint away from straight reference? | Rubbing, play or uncertainty |
|---|---|---|---|
| Centre | Observe | Observe | Record |
| Small movement one way | Observe | Observe | Record |
| Near reviewed thirty-degree limit | Observe | Observe | Record |
| Same movement the other way | Observe | Observe | Record |
Repeat the observations three times. Do not fill the table with calculated values and call them measurements. If viewing angle or joint play makes a small change unclear, record that limitation. We have not physically tested this bench and do not promise a measured accuracy, payload or useful service life.
Why two retained joints matter
A bar connected by only one freely turning joint can change its heading. The second joint closes the linkage and supplies the missing constraint. Neither an animation assigning perfect motion nor fingers holding the bar level can replace it. The linkage idea page explains how joined links constrain one another; the axle guide and bush guide explain why pivot bearings also need axial stops.
The joint shafts themselves need retention. A cap above the blue bar and a stop below the crank prevent the complete joint axle from sliding out through both round holes. Similarly, each main shaft has stops on opposite sides of its fixed frame bearing. Inspect the whole shaft and its attached hardware, rather than checking only whether one beam has a nearby spacer.
If an arm slips on its hub, repair its two mounting pins. If a joint binds, check alignment and seated stops without pinching. If one crank tries to follow a different branch, stop instead of forcing it. The guide has no physical angle stops. Its reviewed small range avoids the flattened positions where this type of linkage can lose a unique continuation; a narrow animation is not extra hardware.
Choose the next question
The Crank Orbit Bench isolates one circular pin path before adding a connecting bar. The Klann Walker uses linkages for a different job: a foot path rather than constant bar heading. Keep those questions separate. First predict direction and path, then make the real comparison, and explain what the visible evidence supports.
Interactive: Check yourself. A few quick questions on the ideas in this guide, each with an explanation.
- What stays parallel in this uncrossed linkage?
- Does a constant bar direction mean its ends move in straight lines?
- What distance matters when choosing connecting-bar holes?
- What should you do if one hub arm slips or a joint cap loosens?
