A Quantified Description of the Coupling between the Reaching Direction and Elbow Axis Direction

Abstract

The human body continues to be an inspiration for the work of a myriad of different fields, both scientific and mathematic. In particular, robotics draws upon the motions and relationships of different human systems in order to reproduce similar mobility while performing different tasks. The human shoulder–arm–elbow complex has been one of the most difficult to exactly replicate. This paper examines the relationship between the motion of the shoulder while positioning the center of the wrist during voluntary arm movements and the resulting orientation of the arm, in particular the direction of the axis passing through the elbow joint. Experimental data is presented that was used to quantify this coupling between the reaching direction of the arm and the elbow axis direction. The results from this paper are two surface‐fit equations that can be used to determine the elbow axis direction when given the location of the wrist center. These results are useful when considering the design and control of shoulder–arm–elbow complex models.

Reproducing Human Arm Motion Using a Kinematically Coupled Humanoid Shoulder–Elbow Complex

“…These constraints approximate the 2:1 ratio between human humeral and scapular rotation. Another two constraints come from Stanisic et al (2007), which couple the direction of the elbow axis to the reaching direction, for voluntary human-reaching motions. Reaching direction is defined as the unit vector directed from the centre of the glenohumeral joint to the wrist centre.…”

“…Step 2: Solve the inverse kinematics problem for θ 3 -θ 6 , implementing the coupling between reaching direction and elbow axis direction found in voluntary human reaching described by Stanisic et al (2007).…”

“…The equations for SP come from concatenating the homogeneous transformations from frame {7} to frame {S}. The values of θ 3 -θ 6 are calculated from a known SP in Equation (2), implementing the two constraints from Stanisic et al (2007) which relate the elbow axis direction to the reaching direction, or the glenohumeral-elbow axis coupling (GE coupling for short). This results in an overconstrained system of five equations in four unknowns, isolating the over-constrained portion of the inverse kinematics problem.…”

“…where 0 S R is the rotation matrix in 0 S T , and 0 S T is known from θ 1 and θ 2 . In order to use the GE coupling as given by Stanisic et al (2007),û is converted to two angles (spherical coordinates) defining the reaching direction (φ reach , θ reach ),…”

“…Then from Stanisic et al (2007), two angles defining the elbow axis direction (φ elbow , θ elbow ), can be determined. This elbow axis direction is then converted back to a unit vector in the anatomical body framê…”