Abstract
In this work the velocity, acceleration, and jerk analyses of a two-degrees-of-freedom parallel wrist are approached by means of the theory of screws. For the sake of completeness, the finite kinematics of the manipulator is also investigated. As far as the authors are aware, the equation of jerk in screw form of the robot at hand is introduced by the first time in this contribution. In order to exemplify the method, a case study is included. The numerical example is verified with the aid of commercially available software.
Highlights
A spherical mechanism is a limited-dof parallel manipulator that has the virtue that all its moving points describe paths forming concentric spherical surfaces
In this work the finite kinematics of a 2-dof parallel wrist is reported in closed-form solution whereas the velocity, acceleration and jerk analyses are approached by means of the theory of screws
A numerical example is provided in order to show the application of the method of kinematic analysis
Summary
A spherical mechanism is a limited-dof parallel manipulator that has the virtue that all its moving points describe paths forming concentric spherical surfaces. Carricato and Parenti-Castelli [2] introduced a novel pointing fully decoupled 2-dof parallel wrist with linear actuators. In this work the finite kinematics of a 2-dof parallel wrist is reported in closed-form solution whereas the velocity, acceleration and jerk analyses are approached by means of the theory of screws. In order to enhance one of the possible applications of the robot at hand it is worth to mention that in an interesting contribution, Novàk [17] studied the motions of subjects turning a knob and concluded that on many trials, subjects turned the knob with a single, smooth, and regular motion as indicated by the angular position and velocity trajectories, but on others cases, subjects produced irregularities in the kinematics, which were considered as discrete corrective submovements, detecting appreciable inflections in the acceleration traces. The jerk analysis would be computed by means of the theory of screws
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