 # Kinematics-forward and inverse analysis.

May 26 • Notes • 2287 Views • 2 Comments on Kinematics-forward and inverse analysis.

KINEMATICS- forward and inverse analysis

Kinematics is thaa branch of mechanics which describes the motion of points , bodies and systems of bodies without considering causes of motion.

ð  It deals with trajectories of points, lines and other geometrical objects and their differential properties. For example: velocity , acceleration.

ð  Study of kinematics is also known as kinematic analysis. This is the process of measuring the kinematic quantities used to describe motion.

Trajectory of a particle

a=dv/dt                     v+dv    dv

particle      dr                     particle

r           r+dr          v=dr/dt

Forward and inverse kinematics:

This concept is best used in robotics.

è The movement of a kinematic chain whether it is a robot or an animated character is decided by the kinematics equation of chain.

è  Forward kinematics:  It uses joint parameters to compute the configuration of the chain.

è Inverse kinematics: It reverses the calculation to determine the joint parameters that achieve a desired configuration.

è It is for constrained system of bodies.

è Kinematic equation of a robot can be used to define the loop equations of a complex articulated system.

è The independent parameters in the equations are known as degrees of freedom.

Application of inverse kinematics:

1)      Interactive manipulation

2)      Animation control

3)      Collision avoidance

4)      Game

5)      3D animation

è An animated figure is structured with a skeleton of rigid segments connected with joints called a kinematic chain.

è Forward  kinematics uses kinematic equation to determine the pose given to the joint angles.

è Inverse kinematics computes the joint angles for desired pose of figure.

JACOBIAN INVERSE TECHNIQUE:

It is a way of implementing inverse kinematics. Let there be ‘n’ variables that govern the forward kinematics equation i.e. the position function. These variables may be joint angles, length or any other arbitrary real values. If the I.K system lives in a 3-dimensional space, the position function can be viewed as a mapping

P(x): Rm  à Rm

P(x0) à initial position of the system

P(x0 + ρ) à the destination point of the system

This technique generates improved estimates of ρ to minimize the error given by ІІ p(x0 +ρ) – p(x0) ІІ

Each one of the intermediate estimates can be added to x0 and evaluated by position function to animate the system.

For small vectors, the series expansion of position function is:

p(x0 +ρ) ~ p(x0) + JP(x0

where  JP(x0) is the (3 * m) jacobian matrix of the position function at x0  .

1)      What is kinematics?

Ans)Kinematics is a branch of mechanics that describes the motion of points , bodies and systems of bodies without considering causes of motion.

2)What is kinematic analysis?

Ans) the process of measuring the kinematic quantities used to describe motion.

3)What is forward kinematics?

Ans) forward kinematics is the branch of kinematics that uses joint parameters to compute the configuration of the chain.

4)What is inverse kinematics?

Ans) Inverse kinematics is the branch of the kinematics which reverses the calculation to determine the joint parameters that achieve a desired configuration.

5)What is a kinematic chain?

Ans) An animated figure is structured with a skeleton of rigid segments connected with joints called a kinematic chain.

6)What is the difference between forward and inverse kinematics?

Ans) Forward  kinematics uses kinematic equation to determine the pose given to the joint angles whereas Inverse kinematics computes the joint angles for desired pose of figure.

6)What is a jacobian inverse technique?

Ans) it is a way of implementing inverse technique to find out the position of a particle.