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##### KINEMATIC CHAINS AND ROBOTS (III)

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**KINEMATIC CHAINS**AND ROBOTS (III)**Kinematic Chains and Robots III**• Many robots can be viewed as an open kinematic chains. This lecture continues the discussion on the analysis of kinematic analysis robots. • After this lecture, the student should be able to: • Solve problems of kinematic analysis using transformation matrices**Link (0): Base**The base is chosen to act as link (0)**Link (1)**Link (0): Base The next link coupled to the base is link (1)**Link (2)**Link (1) The next link coupled to link (1) is link (2)**Link (3): Gripper**Link (2) The next link coupled to link (2) is link (3)**Link (2)**Link (3): Gripper Link (1) Summary of Link Assignment Link (0): Base**Revolute joint <1>**Link (1) Link (0): Base Joint <1> is between link (0) and link (1)**Revolute joint <2>**Link (2) Link (1) Joint <2> is between link (1) and link (2)**Revolute joint <3>**Link (2) Link (3): Gripper Joint <3> is between link (2) and link (3)**Link (2)**Revolute joint <2> Revolute joint <3> Link (3): Gripper Link (1) Revolute joint <1> Summary of Links and Joints Assignment Link (0): Base**Y0**X0 Define the base or reference frame {0} with origin at joint <1>. Notice that Z0 is pointing towards you and X0, Y0, & Z0 form a right hand frame of reference. Note that this base frame is used to describe the global position of the end-effector (or gripper).**X1**Y1 Revolute joint <2> Revolute joint <1> The intersection between the common perpendicular of axes through <2> and <1> with <1> is the origin of frame {1}. X1 points along the common perpendicular from <1> to <2>. Z1 is pointing towards you and defines the axis of rotation of joint <1>. X1, Y1, & Z1 form a right hand frame of reference.**1**X1 Y1 Remember that Z1 is pointing towards you and defines the axis of rotation of joint <1>, i.e. 1 is positive if link (1) rotates counter-clockwise**Y2**X2 Revolute joint <2> Revolute joint <3> The intersection between the common perpendicular of axes through <3> and <2> with <2> is the origin of frame {2}. X2 points along the common perpendicular from <2> to <3>. Z2 is pointing towards you and defines the axis of rotation of joint <2>. X2, Y2, & Z2 form a right hand frame of reference.**2**Y2 X2 Remember that Z2 is pointing towards you and defines the axis of rotation of joint <2>, i.e. 2 is positive if link (2) rotates counter-clockwise**Y3**X3 Revolute joint <3> Choose the origin of frame {3} on axis <3>. Z3 is pointing towards you and defines the axis of rotation of joint <3>. We have selected X3 to point along the length of link <3>. X3, Y3, & Z3 form a right hand frame of reference.**3**Y3 X3 Remember that Z3 is pointing towards you and defines the axis of rotation of joint <3>, i.e. 3 is positive if link (3) rotates counter-clockwise**Y2**X2 Y3 X3 X1, Y0 Y1 X0 Summary of Frame-assignment**Tabulation of D-H parameters**A2 Y2 X2 Y3 X3 A1 Y0 ,X1 Y1 X0 We shall let the above configuration to be called the home position for the robot. A1 and A2 are the lengths of links (1) & (2) respectively**Y0 ,X1**Y1 X0 0 = (angle from Z0 to Z1 measured along X0) = 0° a0 = (distance from Z0 to Z1 measured along X0) = 0 d1 = (distance from X0 to X1 measured along Z1)= 0 1 = (angle from X0 to X1 measured along Z1) 1 = 90° (at home position) but 1 can change as the arm moves**Y2**X2 A1 X1 Y1 1 = (angle from Z1 to Z2 measured along X1) = 0° a1 = (distance from Z1 to Z2 measured along X1) = A1 d2 = (distance from X1 to X2 measured along Z2) = 0 2 = (angle from X1 to X2 measured along Z2) 2 = -90° (at home position) but 2 can change as the arm moves**A2**Y2 X2 Y3 X3 2 = (angle from Z2 to Z3 measured along X2) = 0° a2 = (distance from Z2 to Z3measured along X2) = A2 d3 = (distance from X2 to X3 measured along Z3) = 0 3 = (angle from X2 to X3 measured along Z3) 3= -90° (at home position) but 3 can change as the arm moves**Summary**• Many robots can be viewed as an open kinematic chains. This lecture continues the discussion on the analysis of kinematic analysis robots. • The following were covered: • Kinematic analysis using transformation matrices