Reach is determined jointly by joint range of motion and limb length

What it is

The volume of space a person's hand can reach from a fixed standing or seated position is called the reach envelope, and it's determined by two independent factors together: the length of each limb segment (the absolute size of the upper arm, forearm, and hand) and the range of motion each joint allows (shoulder, elbow, and wrist each have their own limits). These factors act like links chained together in a kinematic chain — the length and rotation range of each link add up along the chain to determine the three-dimensional boundary the fingertip can ultimately trace. Height alone, or the flexibility of any single joint alone, is not enough to derive the actual reach envelope.

Why it happens

The reach envelope isn't a simple sphere because the range of motion at different joints along the kinematic chain is not symmetric in every direction: shoulder flexion typically has a larger range than extension, abduction and adduction aren't equal either, and the elbow can only flex one way — it cannot extend past anatomical straight. These asymmetric limits compound link by link along the chain, so the envelope bulges further out in some directions and is noticeably flattened in others. What limits reach in one direction might be the shoulder joint furthest from the hand, while what limits it in another direction might be the wrist at the far end of the chain — the same person's reach envelope is governed by different joints in different directions, and there is no single "limiting factor."

Studying it

The standard method for measuring a reach envelope is an anthropometry survey combined with motion capture: participants extend to their limit position in each direction from a fixed reference posture, and joint angles and limb-chain lengths are recorded, then used to reconstruct the boundary of the full reachable volume. Large-scale surveys (such as military or industrial anthropometric databases) build percentile tables broken down by sex, age, and population, giving 5th, 50th, and 95th percentile reach distances for designers to select from rather than relying on a single "average" figure.

Where it stops holding

Standard reach-envelope data is usually measured on an unrestrained, normally-postured young adult population and cannot be applied directly to users wearing bulky protective equipment, restrained by a seatbelt or seat, or whose joint range of motion is reduced by age or injury — all of these conditions can substantially shrink the actual reachable range, and the shrinkage isn't necessarily uniform: one direction may be severely restricted while another is barely affected, so generic data cannot simply be scaled down proportionally.

Applying it

• When placing a high-frequency control that nearly all users need to reach, use the smaller end of the population's reach range (such as 5th-percentile data) as the binding constraint, rather than a designer concluding a position is reachable just by reaching for it themselves — this matters especially for cockpits, workbenches, and other fixed-position scenarios.
• For target populations wearing specific equipment or in a restrained posture (seatbelt, wheelchair), use reach data re-measured for that specific scenario rather than applying a generic unrestrained anthropometric table directly.
• Verification: have real participants whose body size falls in the smaller percentile range of the target population attempt to reach the control position being evaluated, in the actual use posture — don't rely on an average-sized designer or a model to judge whether a position is "reachable."

Related

• Same group: A8.25.2 The comfortable reach zone is significantly smaller than the maximum reach zone · A8.25.3 Exceeding the comfort zone requires trunk compensation and breaks stability · A8.25.4 The reach envelope is three-dimensional; flat diagrams underestimate the cost
• Nearby: A8.13 Finger Independence and Strength · C2.11 Thumb Reachable Zone
• Search terms: reach envelope · kinematic chain · anthropometry · range of motion