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The kinematically similar joystick motion is planar.
For example, if an object motion is planar, the dimension of an affine space which includes its trajectories degenerates from 3-D to 2-D.
Although, with very few exceptions, the previous models in the literature make the simplified assumption that this motion is planar, this is usually not true since a body will probably not be aligned with the direction of the ground motion.
Since the motion is planar, and 'p' and L are perpendicular, pz = ηz = 0 and attention may be restricted to the three-dimensional vector \boldsymbol\eta = (ηw, ηx, ηy).
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The relationship between the cam profiles and valve motion is analyzed using planar-cam theory.
Only translational (planar) motion is considered in the input video.
We find that only one planar motion is possible for our system.
We also find parameters for which the planar motion is always stable and hence, whirling motions are not possible.
To apply Kalman filtering for estimating X from Y, we constrain the model with the following assumptions: (i) Only translational (planar) motion is considered in the input video.
A finite element dynamic model of a sliding link through a prismatic joint where the prismatic joint hub is executing general planar motion is formulated.
Beyond the critical amplitude, the planar motion is unstable and we get whirling trajectories which are precessing ellipses again with varying major and minor radii.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com