U21BMP37�ROBOTICS IN MEDICINE

Dr. N. Rajasingam

UNIT - I - INTRODUCTION

Automation and Robots - Classification - Specification - Notations - Direct kinematics - Dot and cross products - Coordinate frames - Rotations - Homogeneous coordinates - Link coordinates - Arm equation - Four-axis robot.

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CO1: Infer with the basics of robotic systems (Understand)

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Automation

• The creation and application of technologies to produce and deliver goods and services with minimal human intervention.
• Over the ensuing decades, specialized machines have been designed and developed for high-volume production of mechanical and electrical parts.

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Hard automation

• When each yearly production cycle ends and new models of the parts are to be introduced, the specialized machines have to be shut down and the hardware retooled for the next generation of models. Since periodic modification of the production hardware is required.
• Here the machines and processes are often very efficient, but they have limited flexibility.

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Soft automation

• Auto industry and other industries have introduced more flexible forms of automation in the manufacturing cycle.
• Programmable mechanical manipulators are now being used to perform such tasks as spot welding, spray painting, material handling, and component assembly.

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• Since computer-controlled mechanical manipulators can be easily converted through software to do a variety of tasks.
• The cost effectiveness of manual labor, hard automation, and soft automation can be qualitatively compared as a function of the production volume.

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Relative cost-effectiveness of automation

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Robot

• A robot is a software-controllable mechanical device that uses sensors to guide one or more end-effectors through programmed motions in a workspace in order to manipulate physical objects.

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Robot Classification

• In order to refine the general notion of a robotic manipulator, it is helpful to classify manipulators according to various criteria such as drive technologies, work envelope geometries and motion control methods.

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Drive Technologies

• One of the most fundamental classification schemes is based upon the source of power used to drive the joints of the robot.
• The two most popular drive technologies are electric and hydraulic.
• Most robotic manipulators today use electric drives in the form of either DC servomotors or DC stepper motors.

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Drive Technologies

• However, when high-speed manipulation of substantial loads is required, such as in molten steel handling or auto body part handling, hydraulic-drive robots are preferred.
• One serious drawback of hydraulic-drive robots lies in their lack of cleanliness, a characteristic that is important for many assembly applications.

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Drive Technologies

• Both electric-drive robots and hydraulic-drive robots often use pneumatic tools or end-effectors, particularly when the only gripping action required is a simple open-close type of operation. An important characteristic of air-activated tools is that they exhibit built-in compliance in grasping objects, since air is a compressible fluid.

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Work-Envelope Geometries

• The end-effector, or tool of a robotic manipulator is typically mounted on a flange or plate secured to the wrist of the robot.
• The gross work envelope of a robot is defined as the locus of points in three-dimensional space that can be reached by the wrist.

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Work-Envelope Geometries

• Major axes: used to determine the position of the wrist.
• Minor axes: used to establish the orientation of the tool.
• Geometry of the work envelope is determined by the sequence of joints used for the first three axes (major).

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Work-Envelope Geometries

• Revolute joints (R): exhibit rotary motion about an axis. They are the most common type of joint.

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• Prismatic joint (P): exhibits sliding or linear motion along an axis. The particular combination of revolute and prism.

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Work-Envelope based on Major axes

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Work-Envelope Geometries

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Cartesian-coordinate Robot

• The three major axes are all prismatic; the resulting notation for this configuration is PPP.
• The three sliding joints correspond to moving the wrist
• up and down
• in and out
• back and forth

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Cartesian-coordinate Robot

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Cartesian-coordinate Robot

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Cartesian-coordinate robot

• It is evident that the work envelope or work volume that this configuration generates is a rectangular box where it also called as rectangular-coordinate robot.
• When a Cartesian-coordinate robot is mounted from above in a rectangular frame, it is referred to as a gantry robot.

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Gantry Robot

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Cylindrical-coordinate Robot

• The first joint of a Cartesian-coordinate robot is replaced with a revolute joint (to form the configuration RPP).
• The revolute joint swings the arm back and forth about a vertical base axis.
• The prismatic joints then move the wrist up and down along the vertical axis and in and out along a radial axis.

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Cylindrical-coordinate Robot

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Cylindrical-coordinate Robot

• Since there will be some minimum radial position, the work envelope generated by this joint configuration is the volume between two vertical concentric cylinders.

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Spherical-coordinate Robot

• The second joint of a cylindrical-coordinate robot is replaced with a revolute joint (so that the configuration is then RRP).
• Here the first revolute joint swings the arm back and forth about a vertical base axis, while the second revolute joint pitches the arm up and down about a horizontal shoulder axis.

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Spherical-coordinate Robot

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Spherical-coordinate Robot

• The prismatic joint moves the wrist radially in and out.
• The work envelope generated in this case is the volume between two concentric spheres.
• The spheres are typically truncated from above, below, and behind by limits on the ranges of travel of the joints.

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Selective Compliance Assembly Robot Arm

• It has two revolute joints and one prismatic joint (in the configuration RRP) to position the wrist.
• However, for a SCARA robot the axes of all three joints are vertical.
• The two revolute joints control motion in a horizontal plane.
• The first revolute joint swings the arm back and forth about a base axis that can also be thought of as a vertical shoulder axis.

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SCARA Robot

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Selective Compliance Assembly Robot Arm

• The second revolute joint swings the forearm back and forth about a vertical elbow axis.
• The vertical component of the motion is provided by the third joint, a prismatic joint which slides the wrist up and down.
• The shape of a horizontal cross section of the work envelope can be quite complex, depending upon the limits on the ranges of travel for the first two axes.

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Articulated-coordinate Robot

• When the last remaining prismatic joint is replaced by a revolute joint (to yield the configuration RRR).
• It is the dual of a Cartesian robot in the sense that all three of the major axes are revolute rather than prismatic.
• It is the most anthropomorphic configuration; that is, it most closely resembles the anatomy of the human arm.

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Articulated-coordinate Robot

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Articulated-coordinate Robot

• Articulated robots are also called revolute robots.
• The first revolute joint swings the robot back and forth about a vertical base axis.
• The second joint pitches the arm up and down about a horizontal shoulder axis.

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Articulated-coordinate Robot

• The third joint pitches the forearm up and down about a horizontal elbow axis.
• These motions create a complex work envelope, with a side-view cross section typically being crescent-shaped.

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Articulated-coordinate Robot

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Motion Control Methods

• Another fundamental classification criterion is the method used to control the movement of the end-effector or tool.
• The two basic types of movement are
• point-to-point motion
• continuous-path or controlled-path motion

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Point-to-Point Motion

• The tool moves to a sequence of discrete points in the workspace.
• The path between the points is not explicitly controlled by the user.
• It is useful for operations which are discrete in nature.
• Ex: spot welding, pick and place, loading and unloading.

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Continuous-Path Motion

• The end-effector must follow a prescribed path in three- dimensional space, and the speed of motion along the path may vary.
• Presents a more challenging control problem.
• Ex: paint spraying, arc welding and the application of glue or sealant.

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Robot Specifications

• There are a number of additional characteristics that allow the user to further specify robotic manipulators.

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Number of Axes

• Each robotic manipulator has a number of axes about which its links rotate or along which its links translate.
• Usually, the first three axes, or major axes, are used to establish the position of the wrist, while the remaining axes are used to establish the orientation of the tool or gripper.

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Number of Axes

• Practical industrial robots typically have from four to six axes.

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Number of Axes

• Since robotic manipulation is done in three-dimensional space, a six-axis robot is a general manipulator in the sense that it can move its tool or hand to both an arbitrary position and an arbitrary orientation within its workspace.
• The mechanism for opening and closing the fingers or otherwise activating the tool is not regarded as an independent axis, because it does not contribute to either the position / orientation.

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Number of Axes

• The redundant axes can be useful for manipulators with more than six axes, as reaching around obstacles in the workspace or avoiding undesirable geometrical configurations of the manipulator.

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Load-carrying capacity

• Load-carrying capacity varies greatly between robots.
• For example, the Mini-mover 5 Microbot, an educational table-top robot, has a load-carrying capacity of 2.2 kg.
• At the other end of the spectrum, the GCA-XR6 Extended Reach industrial robot has a load-carrying capacity of 4928 kg.

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Maximum tool-tip Speed

• The maximum tool-tip speed can also vary substantially between manipulators.
• The Westinghouse Series 4000 robot has a tool-tip speed of 92 mm/sec, while the Adept One SCARA robot has a tool-tip speed of 9000 mm/sec.

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Cycle Time

• The time required to perform a periodic motion.
• The Adept One SCARA robot carrying a 2.2-kg payload along a 700-mm path that consists of six straight-line segments has a cycle time of 0.9 sec.
• Thus the average speed over a cycle is 778 mm/sec, considerably less than the 9000 mm/sec maximum tool-tip speed.

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Reach and Stroke

• The reach and stroke of a robotic manipulator are rough measures of the size of the work envelope.
• Horizontal reach: the maximum radial distance the wrist mounting flange can be positioned from the vertical axis about which the robot rotates.
• Horizontal stroke: the total radial distance the wrist can travel.

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Reach and Stroke

• Thus the horizontal reach minus the horizontal stroke represents the minimum radial distance the wrist can be positioned from the base axis.
• Since this distance is non-negative

Stroke<= Reach

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Reach and Stroke

• Vertical reach: the maximum elevation above the work surface that the wrist mounting flange can reach.
• Vertical stroke: the total vertical distance that the wrist can travel.
• Since this distance is non-negative

Stroke<= Reach

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Reach and Stroke

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Repeatability

• A measure of the ability of the robot to position the tool tip in the same place repeatedly.
• On account of such things as backlash in the gears and flexibility in the links, there will always be some repeatability error, perhaps on the order of a small fraction of a millimeter for a well-designed manipulator.

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Precision

• A measure of the spatial resolution with which the tool can be positioned within the work envelope.

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Accuracy

• A measure of the ability of the robot to place the tool tip at an arbitrarily prescribed location in the work envelope.

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Operating Environments

• The operating environments within which robots function depend on the nature of the tasks performed.
• Often robots are used to perform jobs in harsh, dangerous, or unhealthy environments.
• Ex: transport of radioactive materials, spray painting, welding, and the loading and unloading of furnaces.

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Operating Environments

• The robot must be specifically designed to operate in extreme temperatures and contaminated air.
• In the case of paint spraying, a robotic arm might be clothed in a shroud in order to minimize the contamination of its joints by the airborne paint particles.

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Operating Environments

• Clean room robots are used in the semiconductor manufacturing industry for such tasks as the handling of silicon wafers and photomasks.
• Here the robot is operating in an environment in which parameters such as temperature, humidity, and airflow are carefully controlled.

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Tool Orientation

• Independent minor axes determine the kinds of orientation that the tool or hand can assume.
• Tool orientation convention : yaw-pitch-roll (YPR) system.
• Yaw, pitch, and roll angles have long been used in the aeronautics industry to specify the orientation of aircraft.

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Tool Orientation

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Tool orientation

• Mobile tool coordinate frame M= (m¹, m², m³) is attached to the tool and moves with the tool
• m³ : aligned with the principal axis of the tool and points away from the wrist.
• m² : parallel to the line followed by the fingertips of the tool as it opens and closes.

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Tool orientation

• m¹ : completes the right-handed tool coordinate frame.
• By convention, the yaw, pitch, and roll motions are performed in a specific order about a set of fixed axes.
• Initially, the mobile tool frame M starts out coincident with a fixed wrist coordinate frame F = {f¹, f², f³} attached at the end of the forearm.

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Tool orientation

• First the yaw motion is performed by rotating the tool about wrist axis f¹.
• Next, the pitch motion is performed by rotating the tool about wrist axis f².
• Finally, the roll motion is performed by rotating the tool about wrist axis f³.

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Spherical Wrist

• A robot has a spherical wrist if and only if the axes used to orient the tool intersect at a point.

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NOTATION

• Scalars
• Vectors
• Matrices
• Sets

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NOTATION

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NOTATION

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Column vector

• Represented by arranging its components in an n*1 array and enclosing them in square brackets.

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Column vector

• Superscript T : reserved to denote the transpose of a vector
• The transpose is obtained by interchanging the rows with the columns.
• Thus the transpose of an n*1 column vector is a 1*n row vector, and conversely.

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Column vector

• : denotes the square of the first component of the vector x
• : denotes the first component of the second member of a set of vectors

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Sets

• Curly brackets or braces are used to enclose members of a set.

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Matrices

• Just as a vector can be represented as a one-dimensional array of scalar components, a matrix can be represented by a two-dimensional array of scalar components.

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Matrices

• It is also useful to represent a matrix in terms of its columns.
• Lowercase letter with a superscript index : denote a column of a matrix. [a^j : denotes the j^th column of the matrix A]
• The entire m*n matrix A can be written in terms of its n columns

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Dot and Cross Products

• The dot product of two vectors x and y in Rⁿ is denoted x • y and is defined:

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• The dot product is also called the Euclidean inner product in Rⁿ.
• The matrix transpose operation can be used to express the dot product more compactly as

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Dot Product

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• x and y be arbitrary vectors in Rⁿ
• θ be the angle from x to y.

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Cross Product

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• u and v be arbitrary vectors in Rⁿ
• θ be the angle from u to v.

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Norm

• The norm of a vector x in Rⁿ is denoted as ||x|| and is defined

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Orthogonality

• Two vectors x and y in Rⁿ are orthogonal if and only if

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Completeness

• An orthogonal set of vectors (x¹, x² ..., xⁿ} in Rⁿ is complete if and only if

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Properties

• Nonnegative
• Zero only for the zero vector
• Commutative function
• Linear function

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Cross Product

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Dot and Cross Product

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Direct Kinematics

• A robotic manipulator can be modeled as a chain of rigid bodies called links.
• The links are interconnected to one another by joints.
• One end of the chain of links is fixed to a base, while the other end is free to move.
• The mobile end has a flange or face plate, with a tool or end-effector, attached to it.

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Direct Kinematics

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Direct Kinematics

• There are typically two types of joints which interconnect the links:
• revolute joints: rotational motion about an axis
• prismatic joints: sliding motion along an axis
• The objective is to control both the position and the orientation of the tool in three-dimensional space.

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Direct Kinematics Problem

• The tool or end-effector, can then be programmed to follow a planned trajectory so as to manipulate objects in the workspace.
• In order to program the tool motion, the relationship between the joint variables and the position and the orientation of the tool has to be formulated.

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Coordinates

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Coordinate Frames

• Orthonormal coordinate frames attached to the fixed and the mobile links:

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• Coordinates of p:

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Direct Coordinates Transformation

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Where A

Example: Coordinate Transformation

• For the two coordinate frames in Figure, suppose the coordinates of the point p with respect to the mobile coordinate frame are measured and found to be [p]^M = [0.6, 0.5, 1.4]^T. What are the coordinates of p with respect to the fixed coordinate frame F with the body in the position shown?

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Solution:

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Inverse Coordinates Transformation

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Coordinate Frames

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Fundamental Rotations

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Example: Fundamental Rotation

• Refer to Figure, where the mobile coordinate frame M is rotated about the f1 axis of the fixed coordinate frame F. Let joint angle = π/3 radians be the amount of rotation. Suppose p is a point whose coordinates in the mobile M frame are [p]^M = [2, 0, 3]^T. What are the coordinates of p in the fixed coordinate frame F?

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Solution:

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Example: Fundamental Rotation

• Refer to Figure, suppose q is a point whose coordinates in the fixed coordinate frame F are given by [qJ^F = [3, 4, 0]^T. What are the coordinates of q with respect to the mobile coordinate frame M?

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Solution:

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Composite Rotations

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Composite Rotations

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Yaw-Pitch-Roll matrix [YPR(⍬)]

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Example: Composite Rotation

• Suppose we rotate the tool in Figure about the fixed axes starting with a yaw of π/2 , followed by a pitch of - π/2 and, finally, a roll of π/2. What is the resulting composite rotation matrix?

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Solution:

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Example: Composite Rotation

• Suppose the point p at the tool tip has mobile coordinates [p]^M = [0, 0, 0.6]^T. Find [p]^F following the yaw-pitch-roll transformation.

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Solution:

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Homogeneous Transformation Matrix

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Rotation Matrix

• The 3 X 3 submatrix R in the upper left corner of T.
• It represents the orientation of the mobile coordinate frame relative to the fixed reference frame.

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Translation Vector

• The 3 × 1 column vector p in the upper right corner of T is a translation vector.
• It represents the position of the origin of the mobile coordinate frame relative to the fixed reference frame.

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• The scalar 0 in the lower right corner of T is a nonzero scale factor which is typically set to unity.
• The 1 × 3 row vector η in the lower left corner of T is a perspective vector.

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Fundamental Homogeneous Rotation Matrix

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Example: Homogeneous Rotation

• Suppose that [q]^M = [0, 0, 10, 1]^T represents the homogeneous coordinates of a point located 10 units along the third vector of a mobile coordinate frame M. Suppose that initially M is coincident with a fixed coordinate frame F. If we rotate the mobile M frame by π/4 radians about the first unit vector of F, then find the physical coordinates of the point q in the fixed coordinate frame F.

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Solution:

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Solution:

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Fundamental Homogeneous Translation Matrix

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Example: Homogeneous Translation

• Suppose that [q]^M = [0, 0, 10, 1]^T represents the homogeneous coordinates of a point located 10 units along the third vector of a mobile coordinate frame M. Suppose we translate the mobile M coordinate frame relative to the fixed F coordinate frame by 5 units along the f¹ axis and -3 units along the f² axis. Find the physical coordinates of the point q in the fixed coordinate frame F.

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Solution:

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Example: Composite Transformation

• Let F = {f¹, f² ,f³) and M ={m¹, m², m³) be two initially coincident fixed and mobile orthonormal coordinate frames, respectively. Suppose we translate M along f² by 3 units and then rotate M about f³ by π radians. Find [m¹]^F after the composite transformation.

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Solution:

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Solution:

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Example: Composite Transformation

• Let F = {f¹, f² ,f³) and M ={m¹, m², m³) be two initially coincident fixed and mobile orthonormal coordinate frames, respectively. Suppose we rotate M about f³ by π radians then translate M along f² by 3 units. Find [m¹]^F after the composite transformation.

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Solution:

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Solution:

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• Inverse Rotation:

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• Inverse Translation:

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Inverse Homogeneous Transformation

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Example: Inverse Transformation

• Let F = {f¹, f² ,f³) and M ={m¹, m², m³) be two initially coincident fixed and mobile orthonormal coordinate frames. The homogeneous coordinate transformation matrix which maps mobile M coordinates into fixed F coordinates is given. Find the homogeneous coordinate transformation which maps fixed F coordinates into mobile M coordinates, and use it to find [f²]^M.

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Solution:

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Screw Transformation

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Screw pitch

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• λ = 0: pure rotation with infinite pitch
• ф = 0: pure translation is a screw with a zero pitch
• ρ is positive: screw is right-handed
• ρ is negative: screw is left-handed

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Inverse Screw Transformation

• Screw Transformation:

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• Inverse Screw Transformation:

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Example: Screw Transformation

• Let F = {f¹, f² ,f³) and M ={m¹, m², m³) be two initially coincident fixed and mobile orthonormal coordinate frames, respectively. Suppose we perform a screw transformation along axis f² translating by a distance of λ = 3 and rotating by an angle of π/2. Find [m³]^F following the screw transformation and determine the pitch of the screw.

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Solution:

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Solution:

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Joint parameters

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Link parameters

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Link parameters

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Normal, Sliding and Approach Vectors

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D-H algorithm

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Link-Coordinate Transformation

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Inverse Link-Coordinate Transformation

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Arm Matrix

• Composite homogeneous coordinate transformation matrix to transform from coordinate frame k to coordinate frame k - 1 .
• By multiplying several of coordinate transformation matrices together (Rotation, Translation, Link, Joint)

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Position and Orientation of Tool

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Arm Equation

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Four-axis SCARA Robot (Adept One)

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Position of the Tool tip

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Example: Position of the Tool tip

• Find the position of the tool tip of the Adept One robot when the joint variables are

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Solution:

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