The target as an obstacle:Grasping an object at different heights

Humans use a stereotypical movement pattern to grasp a target object. What is the cause of this stereotypical pattern? One of the possible factors is that the target object is considered an obstacle at positions other than the envisioned goal positions for the digits: while each digit aims for a goal position on the target object, they avoid other positions on the target object even if these positions do not obstruct the movement. According to this hypothesis, the maximum grip aperture will be higher if the risk of colliding with the target object is larger. Based on this hypothesis, we made a set of two unique predictions for grasping a vertically oriented cuboid at its sides at different heights. For cuboids of the same height, the maximum grip aperture will be smaller when grasped higher. For cuboids whose height varies with grip height, the maximum grip aperture will be larger when grasped higher. Both predicted relations were experimentally confirmed. This result supports the idea that considering the target object as an obstacle at positions other than the envisioned goal positions for the digits is underlying the stereotypical movement patterns in grasping. The goal positions of the digits thus influence the maximum grip aperture even if the distance between the goal positions on the target object does not change

Grasping Kinematics from the Perspective of the Individual Digits: A Modelling Study

Grasping is a prototype of human motor coordination. Nevertheless, it is not known what determines the typical movement patterns of grasping. One way to approach this issue is by building models. We developed a model based on the movements of the individual digits. In our model the following objectives were taken into account for each digit: move smoothly to the preselected goal position on the object without hitting other surfaces, arrive at about the same time as the other digit and never move too far from the other digit. These objectives were implemented by regarding the tips of the digits as point masses with a spring between them, each attracted to its goal position and repelled from objects' surfaces. Their movements were damped. Using a single set of parameters, our model can reproduce a wider variety of experimental findings than any previous model of grasping. Apart from reproducing known effects (even the angles under which digits approach trapezoidal objects' surfaces, which no other model can explain), our model predicted that the increase in maximum grip aperture with object size should be greater for blocks than for cylinders. A survey of the literature shows that this is indeed how humans behave. The model can also adequately predict how single digit pointing movements are made. This supports the idea that grasping kinematics follow from the movements of the individual digits

Example set of trajectories generated by the model.

<p>A: Paths of the tips in the horizontal plane. B: A perspective plot of the tips' paths and of the rod on the table. C: Mean velocity profile of both tips. D: Time-course of grip aperture.</p

Approach angles of index finger and thumb when grasping trapezoid-shaped objects.

<p>Black solid squares indicate the experimentally found angles (α in inset, with the standard error across subjects), reproduced from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone-0033150-g004" target="_blank">Fig. 4</a> of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone.0033150-Kleinholdermann1" target="_blank">[75]</a>. The observed angles are more similar to the angles predicted by our model (red lines) than to the angles predicted by the model of Smeets and Brenner (blue lines) or to simple grip closure (grey open circles).</p

Paths of the tips in the horizontal plane for grasping and pointing.

<p>In both the simulation and the experimental study (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone-0033150-g002" target="_blank">Fig. 2</a> of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone.0033150-Smeets5" target="_blank">[76]</a>) the target was a cube (sides of 5 cm) placed at a distance of 30 cm from the digits. To simulate reaching to push on the side of the cube with the index finger, a realistic position was chosen as the goal position of the thumb (1 cm to the side of and 3 cm closer than the goal position of the index finger; indicated with a grey cross).</p

Values chosen for the parameters of the model.

<p>Values chosen for the parameters of the model.</p

Simulating grasping movements to target objects of various sizes.

<p>A: Paths of the tips when grasping a cylinder at an angle of 30 degrees. B: Paths of the tips when grasping a cylinder at an angle of 0 degrees. C: Paths of the tips when grasping a block. D: Mean velocity profiles of both tips when grasping a cylinder at an angle of 30 degrees. E: Mean velocity profiles of both tips when grasping a cylinder at an angle of 0 degrees. F: Mean velocity profiles of both tips when grasping a block. G: Aperture profiles when grasping a cylinder at an angle of 30 degrees. H: Aperture profiles when grasping a cylinder at an angle of 0 degrees. I: Aperture profiles when grasping a block.</p

Simulating a grasping movement in the proximity of obstacles.

<p>Solid red lines represent the condition with no obstacles. Dashed red lines represent the condition with obstacles at ‘b’ and ‘c’. A: Paths of the tips in the horizontal plane. Circles indicate possible obstacle positions. B: Velocity profiles, averaged over both tips. C: Time-course of grip aperture.</p

Results of simulating a grasping movement with a large initial aperture.

<p>The target was a 5.5 cm high cylinder with a diameter of 4 cm placed at a distance of 30 cm on a horizontal surface, as in the experiment by Hesse and Deubel <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone.0033150-Hesse3" target="_blank">[38]</a>. The simulation started with the tips 8 cm apart. A: The position profiles of the tips when simulating grasping. B: The development of aperture in time. The black line represents a single trial of a representative subject measured by Hesse and Deubel (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone-0033150-g003" target="_blank">Fig. 3d</a> of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033150#pone.0033150-Hesse3" target="_blank">[38]</a>). To remove the effect of marker placement in the experimental data, we shifted the emperical curve downwards so that the initial aperture is 8 cm. The red line represents the grip aperture profile given by our model.</p

The effect of changing model parameter values on various measures.

<p>Half the difference in kinematic variable (MV, tMV, MGA, tMGA, MH, tMH and MT) between the outcome for a 10% increase and a 10% decrease of each model parameter (A, R_o, R_t, K, E and D) expressed as a percentage of the original value of the kinematic variable. Results are shown for cylinders with diameters (sizes) of 2 cm and 6 cm. The outcomes that change by more than 5% are printed in bold.</p