In addition, the dimensional formula of kinematic viscosity is \[ML^2T^{-1}\] Hence the dimension of kinematic viscosity is \[L^2T^{-1}\] and the unit is \[m^2s^{-1}\] Kinematic Rotational Motion Formulas The study of motion is known as kinematics. The relationships between rotation...
The five kinematic equations are a set of formulas used to describe the motion of an object in one dimension, also known as linear motion. Each equation relates four variables: displacement (Δx)(Δx), initial velocity (v0)(v0), final velocity (vf)(vf), acceleration (a)(...
Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\\ Lett.\\ B {\\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The calculations are considered all ...
In order to solve the inverse kinematics (IK) of complex manipulators efficiently, a hybrid equilibrium optimizer slime mould algorithm (EOSMA) is proposed. Firstly, the concentration update operator of the equilibrium optimizer is used to guide the anisotropic search of the slime mould algorithm to...
When applying the equations of kinematics for an object moving in one dimension, which of the following statements must be true? (Select all that apply.) a. The velocity of the object must always be in the same direction as its acceleration. b. The accele The object travels 12 m from ti...
Kinematics of Serial Manipulators Serial manipulators are considered simple kinematic chains, i.e., each link can be coupled via one or two joints, to one or two links. The first link is the base and the last link is the end-effector (EE), sometimes called tool. In the sequel, we ...
A single inverse solution branch consists of a set of configurations which have a manifold structure in the joint space of dimension equal to the number of redundant degrees of freedom. The existence of such nontrivial preimage manifolds for redundant DoF manipulators allows configuration motions to ...
(23) and the differential formulas of Eq. (24), the geodesic curvature of ΓP is(25)kgP=sinθP+Rkg*sinδPcosδPR2kg*sin2δP,where kg* in the equation is determined by Eq. (20). If kgP is always constant, ΓP must be a spherical circle. Especially, ΓP is a spherical great ...
It is important to emphasize that, when the\(\tau _i^\nu \)of Eq. (2.6) are rotated to Euclidean space following the procedure outlined in AppendixA, one recovers precisely the basis of [10], given in Eq. (A2). This coincidence, in turn, ensures the unambiguous correspondence (and ...
It is one of the most fundamental problems in robot technology and plays an essential role in robot motion control, trajectory planning, and dynamic a nalysis3. However, the IK of redundant manipulators is a complex problem due to nonlinear E quations4. The traditional methods for ...