COMP322S2000L10

1
Direct Kinematics the Arm Equation (Contd)

• Recall
• Link variables (ak , ak) are constants, i.e.
  characteristics of the arm
• Joint variables (qk , dk) determine the location
  of the frame Lk w.r.t. frame Lk-1
• Let qk denote the kth joint variable,
• qk qk if the kth joint is revolute and
• qk dk if the kth joint is prismatic.
• Let q denote the vector of joint variables.
• For the Rhino 5-axis articulated robot arm,
• q (q1 , q2 , q3 , q4 , q5 )
• For a 4-axis cylindrical robot arm,
• q (q1 , d2 , d3 , q4 )

2
The Arm Equation

• Thus, for a n-axis robot arm, the transformation
  matrix becomes
• R0n(q) p0n(q)
• T0n(q) - - - - - - - - - - - - -
• 0 0 0 1
• where R0n(q) is the orientation of the tool
  frame Lk w.r.t. the base frame L0
• p0n(q) is the position of the tool frame
  Lk w.r.t. the base frame L0
• Example Rhino 5-axis articulated arm (refer to
  class notes for details)

3
Summary of Direct Kinematics

• Given the vector of joint variables (q) and the
  other arm characteristics (e.g. the link
  constants, ak , ak) of a robot arm and the
  configuration of the tool tip w.r.t. the frame
  attached to the tool, the configuration of the
  tool tip w.r.t. the robot base can be determined.
• Question Given the orientation and position of
  the tool in world coordinates, what are the
  values of q ?
• Inverse Kinematics