![]() ![]() True gimbal lock is rare, arising only when two axes are close to perfectly aligned. Thus, any rotation in the Y-axis can also be interpreted as a rotation about the Z-axis. The X-axis rotation also occurs correctly BUT rotates the Z axis onto the Y axis. In such a situation, rotation in the Y-axis is performed first and correctly. In either of these positions the other two axes of rotation become aligned with one another, making it impossible to distinguish them from one another, a singularity occurs and the solution to the calculation of angles becomes unobtainable.įor example, assume that the humerus is being rotated in relation to the thorax in the order Y,X,Z and that the rotation about the X-axis is 90 degrees. Gimbal lock occurs when using Cardan (Euler) angles and any of the rotation angles becomes close to 90 degrees, for example, lifting the arm to point directly sideways or in front (shoulder abduction about an anterior axis or shoulder flexion about a lateral axis respectively). For more information, see Gimbal lock and also Codman's Paradox below. However this may occur in the upper limb and particularly at the shoulder. Fortunately, this does not frequently occur in the joints of the lower limbs during normal or pathological gait. When this happens, one of the possible rotations is lost and becomes unmeasurable. Abduction axis 'floats' so as always to be at right angles to the other two.Ĭardan angles work well unless a rotation approaching 90 degrees brings two axes into line.Rotation is about the rotation axis of the distal element.Flexion is about the flexion axis of the proximal (or absolute) element.Using goniometric definitions, a joint angle is described by the following: In addition to using ordered rotations, joint angles can also be described using goniometric information. The third rotation (rotation) is made about the rotation axis of the moving element. The second rotation (abduction) is made about the abduction axis of the moving element.The other two axes, abduction and rotation, are afterwards no longer aligned in the two elements. The first rotation (flexion) is made about the common flexion axis.This means the segment axes move for absolute rotations and distal segment moves for relative rotations.Ī joint angle is then defined using the following ordered rotations: The proximal segment axes are fixed for relative rotations. For absolute rotations the laboratory axes are fixed. To describe an angle using ordered rotations, the following are true: ![]()
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