This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide theoretical expression inflection congruence, which is equivalent circle planar kinematics. Additionally, introduce new proofs for Euler–Savary and Disteli formulae thoroughly analyze their equivalence.

in this paper, a theoretical approach is proposed, in which spatial distribution of the strength of interplate coupling between two faces of strike-slip faults is investigated in detail through the inverse analysis of synthesized geodetic data. synthesized (or available) geodetic data representing free surface movements is implemented to determine the solution of undertaken inverse problem that...

The paper presents the kinematic model of a new meso-scale (∼1 cm) parallel kinematic machine intended for laser phono-microsurgery of the vocal folds. The proposed mechanism uses the displacement generated by piezoelectric cantilever actuators manufactured via a Smart Composite Microstructure technique. The architecture, the geometry, and the position kinematics of the device, modeled as a spa...

Parameter determination and optimization play an important role for parallel kinematic machines since the machines properties depend significantly on an appropriate choice of the geometry. In this paper, the design of parallel machines is formulated in terms of a global constrained optimization problem, where the constraints are deduced from imperative process requirements e.g. size of the work...

A geometry in the sense of F. Klein’s Erlanger Programm (1872) is a pair (S,G) consisting of a set S and a group G of bijections μ : G → G. The set S is the scene of the geometry, its elements are usually called points. The group G is the geometry’s transformation group. An geometric motion in the geometry (S,G) is a map μ : D → G, t 7→ τt of some domain D ∈ R into the transformation group G. T...

The problem of fault tolerance in cooperative manipulators rigidly connected to an undeformable load is addressed in this paper. Four categories of faults are considered: free-swinging joint faults (FSJFs), locked joint faults (LJFs), incorrectly measured joint position faults (JPFs), and incorrectly measured joint velocity faults (JVFs). Free-swinging and locked joint faults are detected via a...

Kinematic feasibility of a planned robot path is restrained by the kinematic constraints of the robot executing the task, such as workspace, configuration, and singularity. Since these kinematic constraints can be described utilizing the geometry of the given robot, corresponding regions within the robot workspace can be expressed in geometrical representation. Consequently, geometric informati...

The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of th...

The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of th...