PHANTOM Mechanics
In its simplest form, the PHANTOM can be thought of as a transmission between three DC brushed motors with encoders and the human finger. The x, y and z coordinates of the user’s finger tip are tracked with the encoders, and the motors control the x, y and z forces exerted upon the user. Torques from the motors are transmitted through pre-tensioned cable reductions to a stiff, lightweight aluminum linkage. At the end of this linkage is a passive, three degrees of freedom gimbal attached to a thimble. Because the three passive rotational axes of the gimbal coincide at a point, there can be no torque about that point, only a pure force. This allows the user’s finger tip to assume any comfortable orientation. More importantly, because the user can be represented by a single point of friction-less sphere within the virtual environment, collisions and resulting interaction forces within the virtual environment are easily calculated.
The PHANTOM has been designed so that the transformation matrix between motor rotations and endpoint translations is nearly diagonal. Decoupling the three motors produces desirable results in terms of back-drive friction and inertia. For a haptic interface with perceivable inertia and back-drive friction, it is important that the friction and inertia be nearly constant in all directions to minimize the distraction they create for the user (i.e. well conditioned inertia matrix and small, non-disparate friction components) (Vertut, 1986). As interesting design feature of the PHANTOM is that two of the three motors move in such a manner as to counterbalance the linkage structure. Because the PHANTOM is statistically balanced, there is no need to compromise the dynamic range of the device by actively balancing the structure with biased the motor torques. Conveniently, the first rotational axis of the PHANTOM is located directly above the wrist of the user. This permits aligning the inherently spherical workspace of the mechanism with similarly spherical wrist. The complexity of the cable reduction mechanism is minimized by using a single cable to "mesh" two motor capstans with another pulley. This minimizes mechanism width and tensioning difficulty.
http://www.cs.ubc.ca/labs/spin/publications/related/massie94.pdf
The PHANTOM has been designed so that the transformation matrix between motor rotations and endpoint translations is nearly diagonal. Decoupling the three motors produces desirable results in terms of back-drive friction and inertia. For a haptic interface with perceivable inertia and back-drive friction, it is important that the friction and inertia be nearly constant in all directions to minimize the distraction they create for the user (i.e. well conditioned inertia matrix and small, non-disparate friction components) (Vertut, 1986). As interesting design feature of the PHANTOM is that two of the three motors move in such a manner as to counterbalance the linkage structure. Because the PHANTOM is statistically balanced, there is no need to compromise the dynamic range of the device by actively balancing the structure with biased the motor torques. Conveniently, the first rotational axis of the PHANTOM is located directly above the wrist of the user. This permits aligning the inherently spherical workspace of the mechanism with similarly spherical wrist. The complexity of the cable reduction mechanism is minimized by using a single cable to "mesh" two motor capstans with another pulley. This minimizes mechanism width and tensioning difficulty.
http://www.cs.ubc.ca/labs/spin/publications/related/massie94.pdf
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