Choosing joints for a robot wrist

By Tolerance Labs engineering team · Updated 18 October 2026

The wrist sets how a robot arm can orient its tool, and its mass loads every joint behind it. Choosing wrist joints is a trade between torque, speed and range at the tool, and grams that the shoulder must carry.

The three wrist axes

A six-axis arm uses three joints to place the tool and three to orient it. The wrist joints are usually numbered 4, 5 and 6 from the base.

• Wrist 1 rolls the forearm, or in some arms pitches the wrist. It carries the most torque of the three, since the other two wrist joints, the tool and the payload sit beyond it.
• Wrist 2 pitches or yaws the tool. Its load is the tool and payload on a short lever.
• Wrist 3 rolls the tool flange. It carries little gravity torque when the tool is centered, but it sees process torque from tasks such as screwdriving, and it often needs the widest range.

Arms with five axes or fewer drop a wrist joint and accept limits on tool orientation. That is a common choice for picking tasks where the tool always points down.

Torque at the wrist

Wrist torques are small, but the joints must also be small and light. Worked example for wrist 2: a 1.0 kg payload with its center 0.12 m from the wrist 2 axis and a 0.5 kg gripper with its center 0.07 m from the axis.

• Static torque: 1.0 × 9.81 × 0.12 + 0.5 × 9.81 × 0.07 ≈ 1.18 + 0.34 = 1.52 N·m.
• Inertia about the axis: 1.0 × 0.12² + 0.5 × 0.07² = 0.0144 + 0.0025 ≈ 0.017 kg·m².
• At 20 rad/s² of angular acceleration: 0.017 × 20 ≈ 0.34 N·m.
• Peak: 1.52 + 0.34 ≈ 1.9 N·m. With a 1.5 times margin, about 2.8 N·m.

Small joints reach that through high ratios, usually a small harmonic drive of about 50:1 to 100:1. A high ratio holds the tool with little current, gives fine angular resolution, and keeps the motor small. The cost is speed: a motor at 6,000 rpm behind 100:1 gives 60 rpm, about 6.3 rad/s or 360° per second, at the output, before load and voltage limits. Check that the wrist can turn as fast as the task needs. Harmonic vs planetary vs cycloidal reducers compares the reducer types, and the compact joints under 500 g tag lists joints sized for this job.

Why wrist mass multiplies into shoulder torque

A wrist sits at the end of the arm, so its mass acts on the longest lever the shoulder has. Worked example: an arm has its elbow 0.35 m and its wrist center 0.70 m from the shoulder axis. Compare a wrist of three joints and brackets weighing 1.5 kg with one weighing 0.9 kg, with the arm held horizontal.

The 0.6 kg saving frees about 4.1 + 1.8 = 5.9 N·m at the shoulder. For comparison, a 1 kg payload at the same point costs 9.81 × 0.70 ≈ 6.9 N·m of static torque. On small arms the wrist often weighs more than the rated payload, so cutting wrist mass can raise payload almost one for one.

The saving compounds. A lighter wrist lets the elbow be smaller, and a lighter elbow, 0.35 m out, lowers shoulder torque again. Each round is smaller than the last, so two or three passes settle the design. Sizing robot arm joints works through the full arm.

Offset or spherical wrist

In a spherical wrist the three wrist axes meet at one point. The arm’s first three joints then place that point, and the wrist alone sets orientation. Inverse kinematics separates into two simple problems with closed-form solutions. In an offset wrist the axes do not meet. Each joint sits beside the last, often as identical modules bolted at right angles.

Industrial arms often use spherical wrists. Many collaborative and research arms use offset wrists built from identical joint modules, because those are easier to build, repair and stock. Either way, plan paths that avoid the wrist singularity, where small tool motions demand very fast joint motion.

Hollow shafts for tool cables

The tool needs power and data, and sometimes air. Cables that run outside the wrist snag and limit roll range, so most wrists route them through hollow shafts. Hollow-shaft joints and cable routing covers twist, bend radius and slip rings in detail. For a wrist, size the bore from the bundle.

Example bundle: two power conductors and a CAN pair, four wires of 1.5 mm outside diameter, plus one air tube of 4 mm. Area: 4 × π ÷ 4 × 1.5² ≈ 7.1 mm² for the wires and π ÷ 4 × 4² ≈ 12.6 mm² for the tube, about 19.6 mm² in all. A 12 mm bore has π ÷ 4 × 12² ≈ 113 mm², so the bundle fills about 17% of it, which leaves room for the cables to twist. Small wrist joints with bores in this range exist, but the bore is often the first thing to run out in a compact design.

Wrist 3 often needs more than one turn for tasks such as screwdriving. Cable twist limits a hollow joint to a set range; continuous rotation needs a slip ring or a tool with its own power. Check the gripper’s connector and cable needs early; choosing an electric gripper lists them.

Precision and holding at the tool

Wrist play moves the tool on a short lever, so it matters less than play at the shoulder, but it is not zero. Lost motion of 1 arcmin, about 0.00029 rad, at wrist 2 moves a tool point 0.15 m away by 0.15 × 0.00029 ≈ 0.044 mm. The same 1 arcmin at a shoulder 0.85 m from the tool moves it by about 0.25 mm. Small harmonic drives typically have lost motion of about 1 arcmin or less, which is why they are common at the wrist. Backlash and torsional stiffness covers how to measure it.

Also decide what the wrist does when power is lost. A harmonic drive is not self-locking, so a heavy tool held off-axis can turn the wrist as it falls. Some small wrist joints offer a built-in brake; others rely on reducer friction, which may not hold a heavy or long tool. Work out the gravity torque on each wrist axis with the tool at its worst angle, and fit a brake where friction alone does not cover it.

Checklist

• Decide how many wrist axes the task needs and what range each must cover.
• Compute wrist torque from tool and payload mass, lever and acceleration, with margin.
• Check output speed at the chosen ratio against the task.
• Weigh each wrist option and compute its effect on elbow and shoulder torque.
• Choose spherical or offset from kinematics, packaging and the parts you can stock.
• Size hollow bores from the cable and air bundle, and plan for twist or a slip ring at wrist 3.

Browse compact joints under 500 g, harmonic joint modules and robot arm and cobot joints, and compare them in Robot Parts.