Grasping trapezoidal objects

Abstract

When grasping rectangular or circular objects with a precision grip the digits close in on the object in opposite directions. In doing so the digits move perpendicular to the local surface orientation as they approach opposite sides of the object. This perpendicular approach is advantageous for accurately placing the digits. Trapezoidal objects have non-parallel surfaces so that moving the digits in opposite directions would make the digits approach the contact surfaces at an angle that is not 90 degrees . In this study we examined whether this happens, or whether subjects tend to approach trapezoidal objects' surfaces perpendicularly. We used objects of different sizes and with different surface slants. Subjects tended to approach the object's surfaces orthogonally, suggesting that they aim for an optimal precision of digit placement rather than simply closing their hand as it reaches the object.

Fig. 1

Horizontal components of modelled trajectories of the digits towards optimal grasp positions on non-parallel sides. We modelled minimum jerk trajectories (Smeets and Brenner 1999), assuming that the digits either both approach perpendicular to the surface (solid curves) or that they approach in opposite directions (co-linear approach; dotted curves). The definition of the trapezoid angle α and of the approach angle β are indicated

Fig. 2

The experimental set-up as seen from above (a) or from the side (b). Subjects stood upright behind a horizontal surface and performed vertical (downward) grasping movements starting from the end of a downward pointing bar (indicated by the black sphere). They had to lift the grey object and place it onto a small platform. The Optotrak camera on the left in the top view (a) was just above eye height, and is therefore not shown in the side view (b)

Fig. 3

Horizontal projection of the average of all subjects’ trajectories of the thumb (upper curves) and the index finger (lower curves) for grasping 40 mm trapezoidal objects with angles of 110° (left) and 70° (right). Note that the main movement direction was vertical, and is thus not visible in this projection

Fig. 4

Average approach angle β of index finger and thumb. Solid squares indicate the average approach angle for each kind of target (with the standard error across subjects). The continuous line and the open circles indicate the angle predicted by an approach perpendicular to the surface and by an approach along the line connecting the contact points (grip closure), respectively. Grip closure does not predict angles of exactly ±90° because the finger and thumb did not contact the object at exactly symmetrical positions (the prediction is based on the actual contact positions)

Fig. 5

The position of the grasp centre for the various objects (with the standard error across subjects). The grasp centre is the intersection of the grasp-axis (dotted line in inset) with the object’s symmetry axis (dashed line). Positions are relative to the centre of the object’s symmetry axis (open circle in inset; positive is to the right). The continuous lines indicate the position of the trapezoids’ centre of mass relative to the centre of the symmetry axis