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We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
The kinematics recursive equation was built by using the modified D-H method after the structure of rehabilitation lower extremity exoskeleton was analyzed. The numerical algorithm of inverse kinematics was given too. Then the…
In sports analytics, accurately capturing both the 3D locations and rotations of body joints is essential for understanding an athlete's biomechanics. While Human Mesh Recovery (HMR) models can estimate joint rotations, they often exhibit…
This is the second and final article on the tutorial on manipulator differential kinematics. In Part 1, we described a method of modelling kinematics using the elementary transform sequence (ETS), before formulating forward kinematics and…
It is widely expected that the realization of scale invariance in the critical regime implies conformal invariance for a large class of systems. This is known to be true if there exist no integrated operator which transforms like a vector…
Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is…
In experimental robotics, researchers may face uncertainties in parameters of a robot manipulator that they are working with. This uncertainty may be caused by deviations in the manufacturing process of a manipulator, or changes applied to…
This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points…
Mobile manipulators consist of a mobile platform equipped with one or more robot arms and are of interest for a wide array of challenging tasks because of their extended workspace and dexterity. Typically, mobile manipulators are deployed…
The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the…
Conventional robots possess a limited understanding of their kinematics and are confined to preprogrammed tasks, hindering their ability to leverage tools efficiently. Driven by the essential components of tool usage - grasping the desired…
The traditional kinematic calibration method for manipulators requires precise three-dimensional measuring instruments to measure the end pose, which is not only expensive due to the high cost of the measuring instruments but also not…
We present a novel algorithm for collision-free kinematics of multiple manipulators in a shared workspace with moving obstacles. Our optimization-based approach simultaneously handles collision-free constraints based on reciprocal velocity…
Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed…
We illustrate a theoretical procedure determining necessary conditions for which simultaneous pure rolling kinetic constraints acting on a mechanical system can be fulfilled. We also analyze the sufficiency of these conditions by…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…