This paper introduces a novel family of singularityfree kinematically redundant planar parallel mechanisms that have unlimited rotational capabilities. The proposed mechanisms are akin to conventional three-degree-of-freedom planar parallel mechanisms. By introducing a novel kinematically redundant arrangement, four-degree-of-freedom parallel mechanisms are obtained that can completely alleviate singularities and provide unlimited rotational capabilities. The kinematics of the mechanisms are derived, and the Jacobian matrices are obtained. It is shown that the singularities of this type of mechanism are governed by the orientation of a passive link connecting the redundant leg to the platform and that the latter orientation is easily controlled using the kinematic redundancy, thereby alleviating all direct kinematic singularities. An example mechanism is proposed, and a prototype is demonstrated. Example trajectories that include full cycle rotations are shown. The prototype also illustrates the use of the kinematic redundancy for an auxiliary task, namely grasping.Index Terms-Kinematic redundancy, parallel mechanisms, parallel robots, planar mechanisms, singularity.
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Camera calibration is essential for any optical system used to obtain 3D measurements from images. The precision of the 3D depth estimation relies on an appropriate camera model and the accurate estimation of model parameters. These parameters are sensitive to environmental conditions and it is well established that a vision system should be calibrated in operating conditions. This is not always possible since the calibration process is often tedious and time-consuming. Unfortunately, the use of poorly estimated calibration parameters for 3D reconstruction and measurements may lead to suboptimal performance of the system and inaccurate depth estimation. This paper presents a technique using an existing camera model and optical design software to perform calibration simulations. This virtual calibration technique allows for a study of the impact of environmental conditions on the calibration parameters. Using this procedure, it is also possible to predict the statistical behavior of the calibration parameters considering the chosen fabrication processes and tolerances. It can assist vision scientists in the choice of the optical system that best meets the requested precision of the 3D reconstruction. This technique could eventually be integrated in the lens design process to create more reliable optical systems that could be calibrated and used in a range of environmental conditions with a very small variation of their calibration parameters.
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