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Its Jacobian matrix is computed to evaluate the singular positions of the end-effector.
In previous studies, orientable-spindle machines were directly used to generate smooth tool paths traversing singular positions through inverse kinematics.
The end-effector desired trajectory is chosen such that the kinematic and drive singular positions are avoided.
The mechanisms designed using orthogonal 8R or 10R linkages have multiple motion modes and can switch between different modes through singular positions.
It is shown that if certain conditions related to the consistency of the dynamic equations are satisfied by a proper design of the trajectory, the manipulator can pass through the singular positions while the actuator forces and the system motion remain stable.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com