Table 2.

Explanation of variables

${\mathbf{R}}_t^{\prime },{\mathbf{R}}_p^{\prime }$	Orientations of tool (t) and peg (p) at the time of picking with respect to the global coordinates.
Rt, Rp	Orientation of tool (t) and peg (p) at any given time with respect to the global coordinates.
HIP′	Position of the haptic device at the time of picking with respect to the global coordinates.
HIP	Position of the haptic device at any given time with respect to the global coordinates.
${\mathbf{p}}_{pt}^{\prime }$	Relative position of the peg with respect to the tool calculated in the local coordinates of the device at the time of picking.
${\mathbf{p}}_{sp}^{\prime }$	Relative position of the spherical pivot with respect to the local coordinate system of the peg at the time of picking
${\mathbf{p}}_p^{\prime }$	Absolute position of the peg at the time of picking.
${\mathbf{p}}_s^{\prime }$	Absolute position of the spherical pivot at the time of picking.
${\mathbf{p}}_p^t$	Absolute position of the peg’s target.
${\mathbf{p}}_s^p$	Absolute position of the virtual tool after picking.
pp	Position of the peg at any given time after picking.