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Kinematics: Homogeneous Transformation Matrix From Frame-1 To Frame-0 (For The Prismatic Joint)

This document discusses the kinematics and dynamics of a two-link robot arm. It presents the homogeneous transformation matrices that describe the motion of each link. Equations are provided for the forward kinematics, Jacobian, singular configurations, and velocities and accelerations of each link. The dynamics section defines the inertia tensors of each link, kinetic and potential energies, Lagrangian equations, and dynamic equations for the actuators of each joint.

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yihenew01
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39 views15 pages

Kinematics: Homogeneous Transformation Matrix From Frame-1 To Frame-0 (For The Prismatic Joint)

This document discusses the kinematics and dynamics of a two-link robot arm. It presents the homogeneous transformation matrices that describe the motion of each link. Equations are provided for the forward kinematics, Jacobian, singular configurations, and velocities and accelerations of each link. The dynamics section defines the inertia tensors of each link, kinetic and potential energies, Lagrangian equations, and dynamic equations for the actuators of each joint.

Uploaded by

yihenew01
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Kinematics
Homogeneous Transformation Matrix from frame-1 to frame-0 (For the prismatic joint)
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(1)

The origin of joint-1


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(2)

Homogeneous Transformation Matrix from frame-2 to fram-0 (For the Revolute joint)
N.B: theta2(t) = q2(t)
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(3)

Homogeneous Transformation Matrix from frame-2 to fram-0


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(4)
(4)

Forward Kinematics of the robot


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(5)

Jacobian and determinant of end effector position


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(6)

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(7)
Singular Configuration of the robot
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(8)
Velocity of frame-1 with respect to frame-0
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(9)

Velocity of o1
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(10)
Velocity of frame-2 with respect to frame-0
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(11)

The velocity of the end effector or velocity of point P is


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(12)

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(13)

Acceleration of frame-1 with respect to frame-0


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(14)

Composition of the absolute acceleration of link1 and relative acceleration of link 2 with respect to link
1 to obtain the absolute acceleration of link 2:
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(15)

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(17)

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(19)

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(20)

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(21)

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(22)

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(24)

Dynamics
inertia tensor matrix with respect to frame-1 when the mass of the link is concentrated at the center of
the link1
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(25)
(25)

Inertia tensor matrix of link-1 with respect to frame-0


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(26)

Inertia tensor matrix with respect to frame-2 when the mass of the link is concentrated at the center of
the link2
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(27)

Inertia tensor matrix of link-2 with respect to frame-0


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(28)
Direction of gravitational potential energy of link-1 with respect to frame-0
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(29)

Direction of gravitational potential energy of link-2 with respect to frame-0


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(30)

Kinetic energy of Link-1 with respect to frame-0


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(31)

Kinetic energy of Link-2 with respect to frame-0


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(32)

Potential energy of actuator-1 with respect to frame-0


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(33)

Potential energy of actuator-2 with respect to frame-0


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(34)
Lagrangian equation which is the diffrence between total kinetic energy and total potential energy
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(35)

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(36)

dynamic equation for actuator 1


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(37)
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(39)

dynamic equation for actuator 2


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