Kinematics: Workspace : Trajectory:

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Kinematics Workspace Trajectory
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A systematic way to develop the 4x4 matrix
T(q),from Introduction to Robotics, J.J. Craig
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Link i-1
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Axis i-1
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Axis i
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There generally exists a line that connects, and
is perpendicular to, both axes of rotation of a
given member.
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Call the unique length for member i-1 ai-1
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Zi-1 axis is defined to pass through the i-1 axis.
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Xi-1 axis is aligned with the length that defines
ai-1.
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Yi-1 completes the right-handed coordinate system
for member i-1.
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Unless i-1n, (i-1 is the last link or member)
another unique axis ai can be defined.
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di joins ai as a second length parameter for the
ith link.
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di joins ai as a second length parameter for the
ith link.
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The Xi Yi Zi axes are defined according to the
previous scheme.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Four parameters characterize each link For
revolute joints, three are constant and one is
variable.
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Example Forward kinematics for a 3DOF robot
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Example Forward kinematics for a 3DOF robot