PMC

We examined three representations of the kinematic constraints of laparoscopic manipulation. The physically based constraint (left) is consistent with the mechanics of the actual laparoscopic port. The position based (center) and orientation based (right) constraints are mathematical representations that reproduce specific kinematic features of the physical constraint without limiting the physical motion of the hand. The position based constraint removes the contribution of hand rotation, whereas the orientation based constraint removes the contribution of hand translation. Evaluation trials featured the physically based constraint, while training trials featured either position based or orientation based constraints. In the physically based mode, the virtual tool tip (green) follows the full motion of the operator’s input (orange) as constrained by a physical port. In the position based constraint, the virtual tool tip (x_t, y_t, z_t) is defined by a line of length L, constrained through the port (x_p, y_p, z_p) and the hand positions (x_h, y_h, z_h). In the orientation-based constraint, the virtual tool mirrors the orientation (θ_t; ϕ_t) and radial motion (Δr) of the physical tool.

Values of geometric constraint C produced by an external force as time passes. The magnitude of the constraint is represented with color spectrum, from low (blue) to high (red).

Schematic diagram of charge (a) and physical object of shaped charge based on the explosive pressure-coupling constraint principle (b). 1—Truncated cone; 2—spherical segment; 3—restraint cylinder; 4—external explosive column; 5—internal explosive column; 6—shell; 7—booster explosive; 8—detonator; 9—lightning tube socket.

The simplified models for the accessories: (a) The physical model for the clamps and complex constraint; (b) the physical model for the valves and flanges; (c) the physical model for the vibration absorber.