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Hitesh Mohapatra
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KINEMATIC MODEL VS DYNAMIC
MODEL
 TOPICS COVERED:
 Definition
 Forward and inverse models
 Formulation methods
 Uses and applications
KINEMATIC MODEL
 DEFINITION:
 The kinematic model studies the motion of a robot
mechanism regardless of forces
and torque that cause it.
 It allows to compute the position and orientation of
robot manipulator’s end-effector relative to the base of
the manipulator as a function of
the joint variables.
KINEMATIC MODEL
 FORWARD KINEMATIC MODEL:
 The forward kinematic problem asks:
once the joint position, velocity,
acceleration are known, compute the
corresponding variables of the end-
effector in a given reference frame (e.g.
a Cartesian frame).
 The forward kinematic model can be
defined as a function f defined between
the joint space Rn and the work space
Rm:
x=f(q) ; x∈Rm, q∈Rn
KINEMATIC MODEL
 INVERSE KINEMATIC
MODEL:
 Inverse Kinematic Problem:
computation of the relevant
variables (positions, velocities,
accelerations) from the work
space to the joint space.
 Inverse Kinematic Model:
function g=f-1 from Rm to Rn:
q = g(x) = f-1(x); q∈Rn, x∈Rm
KINEMATIC MODEL
 DENAVIT-HARTENBERG NOTATIONS:
 In DH convention notation system, each link can be
represented by two parameters, namely the link length ai
and the link twist angle αi. The link twist angle αi indicates
the axis twist angle of two adjacent joints i and i - 1. Joints
are also described by two parameters, namely the link
offset di, which indicates the distance from a link to next
link along the axis of joint i, and the joint revolute angle Ɵi,
whichis the rotation of one link with respect to the next
about the joint axis .Usually, three of these four parameters
are fixed while one variable is called joint variable.
For a revolute joint, the joint variable is parameter Ɵi, while
for a prismatic joint, it will be di.
KINEMATIC MODEL
 DENAVIT-HARTENBERG NOTATIONS (contd.):
 The four parameters of each link can be specified using DH
notation method. With these parameters, link homogeneous
transform matrix which transforms link coordinate frame i-1 to
frame i.
here sin(Ɵ) is abbreviated as sƟ and cos(Ɵ) as cƟ, Rj denotes rotation about
axis
j, and Tj denotes translation along axis j .
KINEMATIC MODEL
 USES:
 The robotic kinematics is essential for describing an end-
effector’s position, orientation as well as motion of all the
joints.
 In order to deal with the complex geometry of a robot
manipulator, the properly chosen coordinate frames are
fixed to various parts of the mechanism and then we can
formulate the relationships between these frames. The
manipulator kinematics mainly studies how the locations
of these frames change as the robot
joints move.
DYNAMIC MODEL
 DEFINITION:
 Robot dynamics is the study of the relation between the
applied forces/torques and the resulting motion of an
industrial manipulator.
 The dynamic model of a robot studies the relation
between the joint actuator torques
and the resulting motion.
DYNAMIC MODEL
 DIRECT DYNAMIC MODEL:
 Problem: Once the forces/torques applied to the joints,
as well as the joint positions and velocities are known,
compute the joint accelerations.
DYNAMIC MODEL
 INVERSE DYNAMIC MODEL:
 Problem: Once the joint accelerations, velocities and
positions are known, compute the corresponding
forces/torques.
DYNAMIC MODEL
 FORMULATION METHODS:
 There are two commonly used methods for
formulating the dynamics,based on the specific
geometric and inertial parameters of the robot:
 the Lagrange–Euler (L–E) formulation
 the Newton–Euler (N–E) method
 Both are equivalent, as both describe the dynamic
behaviour of the robot motion, but are
specifically useful for different purposes.
DYNAMIC MODEL
 LAGRANGE-EULER FORMULATION:
 The L–E method is based on simple and systematic methods to calculate the
kinetic and potential energies of a rigid body system. The equations of dynamic
motion for a robot manipulator are highly nonlinear, consisting of inertial and
gravity terms, and are dependent on the link physical parameters and
configuration (i.e., position, angular velocity and acceleration).
 This provides the closed form of the robot dynamics, and is therefore
applicable to the analytical computation of robot dynamics, and therefore can
be used to design joint-space (or task-space, using transformation via the
Jacobian) control strategies.
 The L–E formulation may also be used for forward and inverse dynamic
calculation, but this requires the calculation of a large number of coefficients
in M(q) and C(q, q˙), which may take a long time. This makes this method
somewhat unsuitable for online dynamic calculations.
DYNAMIC MODEL
 NEWTON-EULER METHOD:
 The N-E formulation is based on a balance of all the forces acting on the
generic link of the manipulator; this forms a set of equations with a recursive
solution, and was developed. A forward recursion propagates link velocities
and accelerations, then a backward recursion propagates the forces and torques
along the manipulator chain.
 This is developed as a more efficient method than L–E, and is based on the
principle of the manipulator being a serial chain; when a force is applied to one
link, it may also produce motion in connected links. Due to this effect, there
may be considerable duplication of calculation, which can be avoided if
expressed in a recursive form.
 This reduction in computational load greatly reduces calculation time,
allowing the forward and inverse dynamics calculations to be performed in
real-time; therefore, it can enable real-time torque control methods of robot
manipulators.
DYNAMIC MODEL
 USES:
 Dynamics modelling is crucial
for analyzing and synthesizing the dynamic behaviour
of robot.
 An accurate dynamics model of a robot manipulator is
useful in many ways: for the design of motion control
systems, analysis of mechanical design, simulation of
manipulator motion, etc.
KINEMATIC MODEL VS DYNAMIC
MODEL
KINEMATIC MODEL DYNAMIC MODEL
 Studies the motion of a robot
mechanism regardless of
forces and torque that cause
it.
 DH notations are used.
 Essential for describing an
end-effector’s position,
orientation as well as motion
of all the joints.
 Studies the relation between
the joint actuator torques
and the resulting motion.
 LE and NE methods are used.
 Crucial for analyzing and
synthesizing the dynamic
behaviour of robot.

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Kinematic Model vs Dynamic Model

  • 2. KINEMATIC MODEL VS DYNAMIC MODEL  TOPICS COVERED:  Definition  Forward and inverse models  Formulation methods  Uses and applications
  • 3. KINEMATIC MODEL  DEFINITION:  The kinematic model studies the motion of a robot mechanism regardless of forces and torque that cause it.  It allows to compute the position and orientation of robot manipulator’s end-effector relative to the base of the manipulator as a function of the joint variables.
  • 4. KINEMATIC MODEL  FORWARD KINEMATIC MODEL:  The forward kinematic problem asks: once the joint position, velocity, acceleration are known, compute the corresponding variables of the end- effector in a given reference frame (e.g. a Cartesian frame).  The forward kinematic model can be defined as a function f defined between the joint space Rn and the work space Rm: x=f(q) ; x∈Rm, q∈Rn
  • 5. KINEMATIC MODEL  INVERSE KINEMATIC MODEL:  Inverse Kinematic Problem: computation of the relevant variables (positions, velocities, accelerations) from the work space to the joint space.  Inverse Kinematic Model: function g=f-1 from Rm to Rn: q = g(x) = f-1(x); q∈Rn, x∈Rm
  • 6. KINEMATIC MODEL  DENAVIT-HARTENBERG NOTATIONS:  In DH convention notation system, each link can be represented by two parameters, namely the link length ai and the link twist angle αi. The link twist angle αi indicates the axis twist angle of two adjacent joints i and i - 1. Joints are also described by two parameters, namely the link offset di, which indicates the distance from a link to next link along the axis of joint i, and the joint revolute angle Ɵi, whichis the rotation of one link with respect to the next about the joint axis .Usually, three of these four parameters are fixed while one variable is called joint variable. For a revolute joint, the joint variable is parameter Ɵi, while for a prismatic joint, it will be di.
  • 7. KINEMATIC MODEL  DENAVIT-HARTENBERG NOTATIONS (contd.):  The four parameters of each link can be specified using DH notation method. With these parameters, link homogeneous transform matrix which transforms link coordinate frame i-1 to frame i. here sin(Ɵ) is abbreviated as sƟ and cos(Ɵ) as cƟ, Rj denotes rotation about axis j, and Tj denotes translation along axis j .
  • 8. KINEMATIC MODEL  USES:  The robotic kinematics is essential for describing an end- effector’s position, orientation as well as motion of all the joints.  In order to deal with the complex geometry of a robot manipulator, the properly chosen coordinate frames are fixed to various parts of the mechanism and then we can formulate the relationships between these frames. The manipulator kinematics mainly studies how the locations of these frames change as the robot joints move.
  • 9. DYNAMIC MODEL  DEFINITION:  Robot dynamics is the study of the relation between the applied forces/torques and the resulting motion of an industrial manipulator.  The dynamic model of a robot studies the relation between the joint actuator torques and the resulting motion.
  • 10. DYNAMIC MODEL  DIRECT DYNAMIC MODEL:  Problem: Once the forces/torques applied to the joints, as well as the joint positions and velocities are known, compute the joint accelerations.
  • 11. DYNAMIC MODEL  INVERSE DYNAMIC MODEL:  Problem: Once the joint accelerations, velocities and positions are known, compute the corresponding forces/torques.
  • 12. DYNAMIC MODEL  FORMULATION METHODS:  There are two commonly used methods for formulating the dynamics,based on the specific geometric and inertial parameters of the robot:  the Lagrange–Euler (L–E) formulation  the Newton–Euler (N–E) method  Both are equivalent, as both describe the dynamic behaviour of the robot motion, but are specifically useful for different purposes.
  • 13. DYNAMIC MODEL  LAGRANGE-EULER FORMULATION:  The L–E method is based on simple and systematic methods to calculate the kinetic and potential energies of a rigid body system. The equations of dynamic motion for a robot manipulator are highly nonlinear, consisting of inertial and gravity terms, and are dependent on the link physical parameters and configuration (i.e., position, angular velocity and acceleration).  This provides the closed form of the robot dynamics, and is therefore applicable to the analytical computation of robot dynamics, and therefore can be used to design joint-space (or task-space, using transformation via the Jacobian) control strategies.  The L–E formulation may also be used for forward and inverse dynamic calculation, but this requires the calculation of a large number of coefficients in M(q) and C(q, q˙), which may take a long time. This makes this method somewhat unsuitable for online dynamic calculations.
  • 14. DYNAMIC MODEL  NEWTON-EULER METHOD:  The N-E formulation is based on a balance of all the forces acting on the generic link of the manipulator; this forms a set of equations with a recursive solution, and was developed. A forward recursion propagates link velocities and accelerations, then a backward recursion propagates the forces and torques along the manipulator chain.  This is developed as a more efficient method than L–E, and is based on the principle of the manipulator being a serial chain; when a force is applied to one link, it may also produce motion in connected links. Due to this effect, there may be considerable duplication of calculation, which can be avoided if expressed in a recursive form.  This reduction in computational load greatly reduces calculation time, allowing the forward and inverse dynamics calculations to be performed in real-time; therefore, it can enable real-time torque control methods of robot manipulators.
  • 15. DYNAMIC MODEL  USES:  Dynamics modelling is crucial for analyzing and synthesizing the dynamic behaviour of robot.  An accurate dynamics model of a robot manipulator is useful in many ways: for the design of motion control systems, analysis of mechanical design, simulation of manipulator motion, etc.
  • 16. KINEMATIC MODEL VS DYNAMIC MODEL KINEMATIC MODEL DYNAMIC MODEL  Studies the motion of a robot mechanism regardless of forces and torque that cause it.  DH notations are used.  Essential for describing an end-effector’s position, orientation as well as motion of all the joints.  Studies the relation between the joint actuator torques and the resulting motion.  LE and NE methods are used.  Crucial for analyzing and synthesizing the dynamic behaviour of robot.