Robotic Surgery: Remote Center of Motion Arm

Manipulator Arm

Sweep angle 28°

Insertion depth 6.0 cm

Wrist articulation 40°

Sweep speed 1.0×

Kinematics

Lateral force at trocar

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Tip reach

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Shaft angle

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Wrist DOF angle

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How it works

Unlike the tremor-filtering control loop, the defining kinematic feature of a surgical manipulator is spatial: the linkage is built so the instrument shaft always pivots through one fixed point in space — the remote center of motion (RCM), positioned exactly at the trocar where the shaft passes through the body wall.

shaft direction:  d(θ,φ) = rotate(θ, φ) · ẑ
tip position:     p_tip = p_rcm + d(θ,φ)·L_insert + wrist_offset(ψ)
constraint:       every point on the shaft between base and p_rcm
                   sweeps in a cone whose apex is fixed at p_rcm

Because the whole arm — not just the tip — is constrained to rotate about that single fixed apex, the trocar point itself never moves sideways: only the arm's base swings through the sweep angle, the shaft's insertion depth slides straight through the fixed pivot, and a separate wristed end-effector (an "EndoWrist"-style joint) adds the last one or two degrees of freedom right at the tip, independent of the arm's sweep. This is what lets a surgical robot move its instrument freely inside the body while applying essentially zero lateral force to the incision — a mechanical constraint, not a control-loop trick.

Sweep angle — how far the arm's base swings the shaft through the fixed pivot; wider sweeps reach more of the operative field without added risk to the port site.
Insertion depth — how far the shaft extends past the RCM point into the body; deeper insertion lets the wrist reach farther structures.
Wrist articulation — the extra bend at the instrument tip itself, independent of the RCM-constrained shaft; this is where fine dexterity (suturing, dissection angles) actually happens.
RCM constraint sphere — toggles a visual marker at the fixed pivot point, showing that the shaft always threads through the same point in space no matter how the arm sweeps.

Manipulator arm Remote center of motion (trocar) Instrument shaft + wrist Body wall plane

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