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kinematics-2

# kinematics-2 - Movie Segment The Hummingbird IBM Watson...

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1 Movie Segment The Hummingbird, IBM Watson Research Center, ICRA 1992 video proceedings Denavit-Hartenberg Notation •Frame±Attachment Manipulator Kinematics • Link Description • Forward Kinematics Manipulator Base End-Effector Joint axis i Joint axis i -1 Link i -1 Link 1 Link n-1 Link Description a i-1 : Link Length - mutual perpendicular unique except for parallel axis a i-1 == α i-1 Link i-1 Axis i Axis (i-1) α i-1 : Link Twist - measured in the right-hand sense about a i-1 Intersecting Joint Axes The sense of α i-1 is free Axis i-1 α i-1 Axis i Axis i Axis i Axis i

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2 Link i-1 Axis (i-1) a i-1 == α i-1 Axis i } d i a i θ i d i : Link Offset -- variable if joint i is prismatic θ i : Joint Angle -- variable if joint i is revolute Link Connections First & Last Links Axis i Axis i+1 α i a i a i and α i depend on joint axes i and i+1 a 1 , a 2 ... a n-1 and α 1 , α 2 ... α n-1 Axes 1 to n: determined a 0 = a n = 0 and α 0 = α n = 0 Convention: First Link Axis 0 α 0 α 0 0 Axis 2 Axis 1 α 1 a 1 } d 1 θ 1 a 0 Axis 0 a 0 = 0 and α 0 = 0 End-Efector Frame {0} 1 0 n + 0 n Last Link Axis n α n a n } d n θ n a n-1 Axis n-1 Axis n+1 Axis n+1 Axis n+1 a n = 0 and α n = 0 First & Last Links Axis i Axis i+1 α i a i } d i θ i a i-1 θ i and d i depend on links i-1 and i θ 2 , θ 3 , . .. , θ n-1 d 2 , d 3 , . .. , d n-1 and Following joint type: d 1 or θ 1 = 0 and d n or θ n = 0 Convention: set the constant parameters to zero
3 First Link Axis 0 α 0 α 0 Axis 2 Axis 1 α 1 a 1 } d 1 θ 1 a 0 Axis 0 d 1 or θ 1 = 0 Last Link Axis n α n a n } d n θ n a n-1 Axis n-1 Axis n+1 Axis n+1 Axis n+1 d n or θ n = 0 Denavit-Hartenberg Parameters 3 fixed link parameters α i and a i : describe the Link i d i and θ i : describe the Link’s connection 1 joint variable θ i revolute joint d i prismatic joint i , a i , d i , θ i ) 4 D-H parameters

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kinematics-2 - Movie Segment The Hummingbird IBM Watson...

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