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The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily derived from the general transport equation for property Φ by deleting transient and convective terms [1]
Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics. [2] [3] More recently, many practical heuristic algorithms based on stochastic optimization and iterative sampling were developed, by a wide range of authors, to address the kinodynamic planning problem. These ...
An analytic solution to an inverse kinematics problem is a closed-form expression that takes the end-effector pose as input and gives joint positions as output, = (). Analytical inverse kinematics solvers can be significantly faster than numerical solvers and provide more than one solution, but only a finite number of solutions, for a given end ...
A configuration describes the pose of the robot, and the configuration space C is the set of all possible configurations. For example: If the robot is a single point (zero-sized) translating in a 2-dimensional plane (the workspace), C is a plane, and a configuration can be represented using two parameters (x, y).
The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses. An exact solution in two spatial dimensions is known, and is presented below. Animation of a Taylor-Green Vortex using colour coded Lagrangian tracers
Paden–Kahan subproblems are a set of solved geometric problems which occur frequently in inverse kinematics of common robotic manipulators. [1] Although the set of problems is not exhaustive, it may be used to simplify inverse kinematic analysis for many industrial robots. [2] Beyond the three classical subproblems several others have been ...
The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters values. Remarkably, while the forward kinematics of a serial chain is a direct calculation of a single matrix equation, the forward kinematics of a parallel chain requires the simultaneous solution of multiple matrix ...
Kinematics; Inverse kinematics: a problem similar to Inverse dynamics but with different goals and starting assumptions.While inverse dynamics asks for torques that produce a certain time-trajectory of positions and velocities, inverse kinematics only asks for a static set of joint angles such that a certain point (or a set of points) of the character (or robot) is positioned at a certain ...