![]() ![]() This leads to vibrations and ultimately limits the maximum speeds. At the same time, to ensure a uniform speed of the extruder, significant accelerations are required along the individual rods. The analysis showed that the average speed of movement of the extruder is approximately equal to, and in some cases less than the linear speeds of movements along the rods. For this, the displacements and velocities were simulated for four examples of motion trajectories. The article attempts to understand the advantages and disadvantages of delta kinematics for use in 3D printers. However, delta kinematics has received limited application, mainly for personal FDM printers. Traditionally, delta kinematics are considered to have advantages over sequential linear kinematics due to their high travel speed and relatively low cost. Improvements in printers are needed to improve accuracy and productivity. This advantage is effectively used in the manufacture of small batches of products with complex surfaces in the automotive and aviation industries. Finally, the inverse kinematics of 7 DoF redundant manipulators with a spherical wrist is solved by extending the geometric solutions obtained in the non-redundant case.Īdditive manufacturing makes it possible to speed up the process of manufacturing a product using a CAD model many times over. ![]() The latter is solved by appropriately splitting the rotor that defines the target orientation in three simpler rotors, while the former is solved by developing a geometric strategy for each combination of prismatic and revolute joints that forms the position part of the robot. For serial robots of this kind, the inverse kinematics problem can be split in two subproblems: the position and orientation problems. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time, or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. This work addresses the inverse kinematics of serial robots using conformal geometric algebra. This distance function is used to enhance how the singularities are handled in three different scenarios, namely, motion planning, motion control and bilateral teleoperation. In addition, since rotors represent rotations in geometric algebra, once these singularities have been identified, a distance function is defined in the configuration space C, such that its restriction to the set of singular configurations S allows us to compute the distance of any configuration to a given singularity. In particular, it consists of identifying which configurations cause the exterior product of these twists to vanish. While classical approaches entail the computation of the determinant of either a 6×n or n×n matrix for an n-degrees-of-freedom serial robot, this work addresses a novel singularity identification method based on modelling the twists defined by the joint axes of the robot as vectors of the six-dimensional and three-dimensional geometric algebras. Hence, their identification is fundamental to enhance the performance of current control and motion planning strategies. The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. ![]()
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