Unit 1: Robot Anatomy - Subjective Questions

Robot anatomy is the study of the physical structure and arrangement of a robot. It describes how the following components are connected and operate:

• Links: Rigid members that form the body of the robot.
• Joints: Mechanical connections that permit relative motion between links.
• Actuators: Devices such as motors or pneumatic cylinders that produce motion.
• End-effector: The tool or gripper attached to the final link.
• Controller: The system that coordinates actuator movements.

Studying robot anatomy helps determine the robot's motion capabilities, workspace, degrees of freedom, and limitations. In a laboratory, it also helps students identify the maximum and minimum positions of links and visualize how individual joint motions contribute to the overall movement of the robot.

A link is a rigid or nearly rigid member of a robot manipulator that connects two successive joints. Links transmit motion and forces from one joint to another.

The position of an end-effector depends on:

• The lengths of all links.
• The orientation of each link.
• The displacement of the connected joints.
• The type and arrangement of the joints.

For a planar two-link robot, the end-effector position can be expressed as:

where and are link lengths and and are joint angles. Thus, links provide the geometric structure required to position and move the end-effector.

The maximum position of a link is the extreme position reached in a particular direction or coordinate, while the minimum position is the opposite extreme position permitted by the robot mechanism.

These positions can be determined experimentally by:

1. Placing the robot in its reference or home position.
2. Identifying the joint associated with the link under study.
3. Moving the joint slowly in the positive direction until its mechanical or software limit is reached.
4. Recording the link position or joint angle as the maximum value.
5. Returning the joint to the reference position.
6. Moving it in the negative direction until the opposite limit is reached.
7. Recording the minimum value.

The values must be measured without forcing the joint beyond its permitted range. The measured limits define part of the robot's workspace and help prevent collisions and mechanical damage.

Joint limits and workspace limits describe different restrictions:

• Joint limits: These are the minimum and maximum allowed values of an individual joint variable. They may be caused by mechanical stops, actuator limitations, cable routing, or controller settings.
• Workspace limits: These define the region in space that the robot end-effector can reach. They depend on link lengths, joint limits, joint arrangement, and obstacles.

A joint limit is usually expressed as:

for a revolute joint, or:

for a prismatic joint.

Joint limits are restrictions on robot variables, whereas workspace limits are restrictions on the resulting position and orientation of the end-effector. A workspace may be smaller than the theoretical geometric workspace because of these joint restrictions.

The procedure for determining the angular limits of a revolute joint is as follows:

1. Switch on the robot and initialize it according to the laboratory procedure.
2. Place the robot in its home or reference configuration.
3. Select the revolute joint to be examined.
4. Move the joint slowly in the positive angular direction.
5. Stop when the mechanical, software, or safety limit is reached.
6. Record the maximum angle using the controller, display, or measuring instrument.
7. Return the joint to its reference position.
8. Move the joint slowly in the negative direction.
9. Record the minimum angle .
10. Repeat the measurement to check consistency.

The final range is written as:

The joint should never be forced against a mechanical stop, and emergency-stop procedures must be available during the experiment.

The extreme positions of robot links are influenced by several mechanical and control factors:

• Mechanical stops: Physical barriers restrict joint rotation or translation.
• Software limits: The controller may impose safe limits that are smaller than the mechanical range.
• Link dimensions: Link lengths affect the distance reached by the end-effector.
• Joint type: Revolute joints provide angular motion, while prismatic joints provide linear motion.
• Cable and hose routing: Excessive movement can stretch, twist, or damage cables and hoses.
• Collisions: Adjacent links may interfere with one another.
• Actuator capacity: Motor torque or force can limit practical movement.
• Payload: A heavy payload may reduce the usable range or accuracy.
• Singular configurations: Certain positions may cause poor control or loss of independent motion.

Therefore, the practical position range is determined by both the robot's geometry and its safety and operating constraints.

Degrees of freedom (DOF) is the number of independent variables required to completely specify the position and orientation of a robot or its end-effector.

Examples include:

• One revolute joint contributes one rotational DOF.
• One prismatic joint contributes one translational DOF.
• A planar body can generally have three DOF: translation along , translation along , and rotation about the perpendicular axis.
• A free rigid body in three-dimensional space can have six DOF: three translations and three rotations.

DOF is important because it indicates how many independent motions a robot can perform. A robot with more DOF can reach more positions and orientations, but it usually requires more complex control and may have a larger mechanical structure. In the laboratory, DOF analysis helps identify which joints contribute to the movement observed in the Sierena's Perro and Twist robots.

DOF can be visualized by observing and recording the independent motions produced by each joint.

A suitable procedure is:

1. Identify all links and joints of the robot.
2. Move only one joint while keeping the remaining joints fixed.
3. Observe whether the motion is rotational or translational.
4. Mark the axis and direction of the motion.
5. Repeat the process for every joint.
6. Combine the individual joint motions to observe the complete movement of the robot.
7. Record the resulting end-effector position and orientation.

A joint contributes an independent DOF only if its motion is not completely constrained by another joint. The visualization may be performed using physical observation, a robot simulation, a coordinate frame display, or a plotted motion path. The experiment should clearly show how each DOF changes the location or orientation of the robot's links and end-effector.

The DOF visualization procedure for the Sierena's Perro robot can be carried out as follows:

• Inspect the robot and identify its links, joints, actuators, and end-effector.
• Establish the home configuration and define a reference coordinate frame.
• Label each joint in sequence from the base toward the end-effector.
• Operate one joint at a time while holding all other joints fixed.
• Observe the type of motion produced by each joint and identify its axis.
• Record the corresponding joint variable, such as an angle or displacement.
• Move combinations of joints to observe how their motions add together.
• Trace the path of the end-effector for selected joint movements.
• Compare the observed motion with the expected motion based on the robot's construction.

The resulting joint-motion diagram or simulation provides a visual representation of the robot's DOF and shows how the links contribute to its reachable workspace.

The DOF of the Twist robot can be visualized using the following steps:

1. Place the robot in its reference position.
2. Identify every link and joint from the base to the end-effector.
3. Determine whether each joint produces rotation, translation, or another constrained motion.
4. Activate one joint at a time and observe the motion of the succeeding links.
5. Mark the axis, direction, and approximate range of each motion.
6. Record the change in the end-effector position and orientation.
7. Activate multiple joints sequentially to study combined motion.
8. Display or sketch the robot configurations at selected joint values.
9. Compare the observed motion with the expected kinematic behavior.

This procedure makes it possible to distinguish independent joint motions from motions that are coupled or constrained by the robot's mechanism.

The Sierena's Perro and Twist robots can be compared by examining their structure and independent joint motions.

The exact DOF count must be obtained from the physical or simulated robot configuration. In both cases, a DOF is counted only when it represents an independent controllable motion.

Consider a planar two-link robot with link lengths and , and joint angles and . The first link is measured from the base, while the second link is measured relative to the first link.

The position contributed by the first link is:

The orientation of the second link with respect to the fixed reference axis is . Therefore, its contribution is:

Adding the two contributions gives the end-effector position:

By substituting the minimum and maximum joint angles into these equations, the corresponding extreme positions can be estimated and plotted.

For a two-link planar robot, the workspace is the set of all positions reached by varying and within their permitted limits:

The end-effector coordinates are calculated using:

To estimate the workspace:

• Select several values of within its allowed range.
• Select several values of within its allowed range.
• Calculate and for every pair of angles.
• Plot the resulting points.
• Join or fill the boundary points to obtain the approximate reachable region.

If both joints can rotate freely through suitable ranges, the workspace may resemble an annular region. Restricted joint angles produce a smaller sector or irregular region.

Revolute joints and prismatic joints are the two basic types of single-DOF joints.

• A revolute joint permits angular movement about a fixed axis. Its joint variable is an angle, usually represented by . Examples include elbow and shoulder rotation.
• A prismatic joint permits linear movement along a fixed axis. Its joint variable is a displacement, usually represented by . Examples include telescoping or sliding mechanisms.

Both joints normally contribute one DOF, but their effects on link positions are different. Revolute motion changes the orientation of a link and usually moves its endpoint along an arc. Prismatic motion changes the distance between links and moves an endpoint along a straight line.

The type of joint must be identified when visualizing DOF and determining maximum and minimum link positions.

A robot's link position is described relative to coordinate frames assigned to the base and successive links. Each joint variable determines the transformation from one frame to the next.

For a revolute joint, the variable is generally the angle . For a prismatic joint, it is generally the displacement . The link geometry and joint variable together determine the position and orientation of the next link.

The overall transformation from the base to the end-effector is obtained by multiplying the individual transformations:

Here, represents the transformation between two consecutive link frames. This relationship is useful in the laboratory because changing one joint variable changes the associated link frame and may also change the positions of all subsequent links.

A joint coordinate system is a representation in which the configuration of a robot is specified by its joint variables. These variables may be joint angles for revolute joints or linear displacements for prismatic joints.

For a robot with joints, its configuration can be represented as:

where each is an independent joint variable.

Joint coordinates help laboratory measurements because:

• Each joint can be calibrated separately.
• Minimum and maximum limits can be recorded numerically.
• The robot configuration can be repeated accurately.
• Link positions can be related directly to actuator readings.
• Workspace boundaries can be calculated from joint limits.

They also provide a convenient way to compare the actual motion of a robot with its programmed or theoretical motion.

The home position is a predefined reference configuration of a robot. It is important because it provides a common starting point for observation, measurement, and programming.

Its uses include:

• Establishing the zero or reference value of joint variables.
• Providing a known configuration before an experiment begins.
• Making maximum and minimum measurements repeatable.
• Helping identify the direction of positive and negative joint motion.
• Reducing the chance of unexpected collisions during initialization.
• Allowing the results from different trials or robots to be compared.

When determining link limits, the operator should first move the robot to its home position, confirm that the coordinate readings are correct, and then move each joint gradually toward its permitted extremes. Without a reliable reference position, measured limits may be inconsistent or incorrectly interpreted.

Maximum and minimum link positions can be represented graphically by plotting the link or end-effector at its extreme configurations.

A typical graphical method is:

1. Draw the base coordinate frame.
2. Draw the robot in its home position.
3. Move the selected joint to its minimum value and draw the resulting link configuration.
4. Move the joint to its maximum value and draw the second configuration.
5. Mark the positions of the joint, link endpoint, and end-effector.
6. Connect the endpoint positions or plot the complete trajectory between them.

For a revolute joint, the endpoint generally follows an arc. For a prismatic joint, it generally follows a line segment. If several joints are varied, the plotted points form part of the robot's workspace. Graphical representation makes the motion range and possible collisions easier to identify than numerical data alone.

Actuators and sensors perform complementary functions in position-limit experiments.

• Actuators: Motors, servos, or pneumatic devices generate the force and motion required to move the joints.
• Position sensors: Encoders, potentiometers, or resolvers measure joint angle or displacement.
• Limit switches: Detect when a joint reaches a physical or predefined boundary.
• Controller: Reads sensor feedback and stops or restricts motion when a limit is reached.

The actuator moves a link, while the sensor provides the measured joint variable. If the measured variable reaches or , the controller can prevent further movement. Sensor feedback also allows the link position to be displayed in a simulation or plotted against time.

Accurate calibration is essential because sensor offset, backlash, and measurement noise can cause the recorded limits to differ from the actual mechanical limits.

A singular configuration is a robot posture in which one or more independent directions of end-effector motion become unavailable or indistinguishable. Mathematically, it occurs when the robot Jacobian loses rank or its determinant becomes zero for a square Jacobian.

The Jacobian relates joint velocities to end-effector velocities:

At a singularity:

• Some joint motions may produce nearly the same end-effector motion.
• The robot may lose effective DOF in a particular direction.
• Very large joint velocities may be required for a small Cartesian motion.
• Position control may become inaccurate or unstable.
• The visualized workspace boundary may contain a cusp, fold, or restricted direction.

During the laboratory experiment, singular postures should be identified and approached carefully. A robot may still have the same number of physical joints, but its effective motion capability is reduced at the singular configuration.