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1. The DenavitHartenberg parameters (also called DH parameters) are the four parameters

associated with a particular convention for attaching reference frames to the links of a spatial

kinematic chain, or robot manipulator. A commonl used convention for selecting frames of

referencein roboticsapplications is the Denavit and Hartenberg (DH) conventionwhich was

introduced b !ac"ues Denavitand#ichard $. Hartenberg.%n this convention, coordinate frames

are attached to the &oints between two links such that one transformationis associated with the&oint, ', and the second is associated with the link '*.

+. Kinematics anales the geometr of a manipulator, robot or machine motion. The essentialconcept is aposition.

Kinematics terminology:

Link is the rigid part of the robot bod (e.g. forearm).

Joint is a part of the robot bod which allows controlled or free relative motion

of two links (connection element).

End effector is the link of the manipulator which is used to hold the tools (gripper, spra gun,

welding gun...).Base is the link of the manipulator which is usuall connected to the ground and is directl

connected to the world coordinate sstem.

Kinematic pair is a pair of links which relative motion is bounded b the &oint connecting them

(e.g. base and shoulder connected b !1 a-is).

. Degrees of freedom (D/0) is a term used to describe a robots freedom of motion in threedimensional space2specificall, the abilit to move forward and backward, up and down, and tothe left and to the right. 0or each degree of freedom, a &oint is re"uired. A robot re"uires si-

degrees of freedom to be completel versatile. The number of degrees of freedom defines the

robots configuration.

The three degrees of freedom in the robot arm are the rotational traverse, the radial

traverse, and the vertical traverse. The rotational traverse is movement on a vertical a-is. This is

the side3to3side swivel of the robots arm on its base. The radial traverse is the e-tension andretraction of the arm, creating in3and3out motion relative to the base. The vertical traverse

provides up3and3down motion. 0or applications that re"uire more freedom, additional degrees can

be obtained from the wrist, which gives the end effector its fle-ibilit. The three degrees of

freedom in the wrist have aeronautical names4 pitch, aw, and roll. The pitch, or bend, is the up3

and3down movement of the wrist. Theyaw is the side3to3side movement, and the roll, or swivel,

involves rotation.

5. The controller is the part of a robot that coordinates all movements of the mechanical sstem. %t

also receives input from the immediate environment through various sensors. The heart of the

http://en.wikipedia.org/wiki/Kinematic_chainhttp://en.wikipedia.org/wiki/Robothttp://en.wikipedia.org/wiki/Frames_of_referencehttp://en.wikipedia.org/wiki/Frames_of_referencehttp://en.wikipedia.org/wiki/Roboticshttp://en.wikipedia.org/wiki/Roboticshttp://en.wikipedia.org/wiki/Robotics_conventions#Denavit.E2.80.93Hartenberg_link_frame_convention_.28DH.29http://en.wikipedia.org/wiki/Robotics_conventions#Denavit.E2.80.93Hartenberg_link_frame_convention_.28DH.29http://en.wikipedia.org/w/index.php?title=Jacques_Denavit&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Richard_S._Hartenberg&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Richard_S._Hartenberg&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Richard_S._Hartenberg&action=edit&redlink=1http://en.wikipedia.org/wiki/Transformation_(geometry)http://en.wikipedia.org/wiki/Kinematic_chainhttp://en.wikipedia.org/wiki/Robothttp://en.wikipedia.org/wiki/Frames_of_referencehttp://en.wikipedia.org/wiki/Frames_of_referencehttp://en.wikipedia.org/wiki/Roboticshttp://en.wikipedia.org/wiki/Robotics_conventions#Denavit.E2.80.93Hartenberg_link_frame_convention_.28DH.29http://en.wikipedia.org/w/index.php?title=Jacques_Denavit&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Richard_S._Hartenberg&action=edit&redlink=1http://en.wikipedia.org/wiki/Transformation_(geometry)

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robots controller is generall a microprocessor linked to input6output and monitoring devices.

The commands issued b the controller activate the motion control mechanism, consisting of

various controllers, amplifiers, and actuators. An actuator is a motor or valve that converts power

into robot movement. This movement is initiated b a series of instructions, called a program,

stored in the controllers memor. The controller has three levels of hierarchical control.

Hierarchical control assigns levels of organiation to the controllers within a robotic sstem. 7achlevel sends control signals to the level below and feedback signals to the level above. The levels

become more elemental as the progress toward the actuator. 7ach level is dependent on the level

above it for instructions.

The three levels are4

8evel %2Actuator 9ontrol. The most elementar level at which separate movements of the robot

along various planes, such as the *, :, and a-es are controlled.

8evel %%2;ath 9ontrol. The path control (intermediate) level coordinates the separate movements

along the planes determined in 8evel % into the desired tra&ector or path.

8evel %%%2. ?inematics 9ause of motion not considered.Dnamics

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?anes formulation @ 9hoose generalised coordinates and speeds, obtain generalised active and

inertia forces, and e"uate the active and inertia forces.

7uler @ 8agrange Approach4

@ Develops a B8agrangian 0unctionC which relates ?inetic and ;otential 7nerg of the

manipulator, as it is moving, thus dealing with the manipulator BAs a holeC in building

force6tor"ue e"uations

ewton @ 7uler Approach4

@ This approach works to separate the effects of each link on machine tor"ues b writing

down its motion in a separable linear and angular sense. However, due to the highl

coupled motions in a robot, it re"uires a forward recursion through the entire manipulator

for building velocit and acceleration models of a link followed b a backward recursion

for force and tor"ue on each link Ein turn

F. !A9/G%A4 Gecause we control the robot in &oint space and tend to reason about motion in9artesian space, we need to full understand the mapping from &oint space to 9artesian space and

vice3versa. 0orward and inverse kinematics describes the static relationship between these

spaces, but we must also understand the differential relationships.

To do this, we will define a mapping between small (differential) changes in &oint space

and how the create small (differential) changes in 9artesian space. The matri- which relates

changes in &oint parameter velocities to 9artesian velocities is called the !acobian

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LMs in 5throw e-cept for 1 in 5,5 position.