Experiment 1: Manipulator Kinematics & Anatomy of Cobot-C1

Explore how joint movements translate into end-effector positions in both simulation and real-world settings.

Objectives

Understand how joint angles and link lengths determine end-effector position and orientation
Investigate how link lengths and joint constraints define the reachable workspace
Practice inputting specific joint angles and observing the resulting manipulator pose

Key Concepts

Manipulator Kinematics - Relationship between joint angles and end-effector position/orientation
Robot Components - Links, joints, manipulators, wrists, end-effectors, actuators, sensors, and controllers
Degrees of Freedom (DOF) - Understanding 6-DOF configuration for spatial manipulation
Denavit-Hartenberg (DH) Convention - Systematic method for assigning coordinate frames
DH Parameters - Four parameters (a, α, d, θ) describing robot geometry
Transformation Matrices - Mathematical representation of robot kinematics
Workspace Analysis - Understanding reachable positions based on robot configuration

Theory

Robot Components

Links: Individual rigid bodies that make up the robot. Links are rigid members that may have relative motion with respect to other links.

Joints: Connections between two links where relative motion occurs. Joints are typically revolute (rotary) or prismatic (translational).

Manipulator: The main body of the robot, consisting of links, joints, and other structural elements.

Wrist: The section between the arm and end-effector, typically the last few joints. Often takes the form of a spherical wrist with three intersecting rotary joints.

End-effector: The tool or gripper mounted on the last link, responsible for performing the robot's tasks.

Actuators: The "muscles" of the robot, providing motion at each joint. May be electric, hydraulic, or pneumatic motors.

Sensors: Devices that detect joint position, velocity, acceleration, or force, providing feedback for control.

Controller: The decision-making unit responsible for collecting sensor information and coordinating movement.

Degrees of Freedom

A robot manipulator is comprised of a sequence of links connected by joints to form a kinematic chain. The degree of freedom (DOF) is the number of independent coordinates required to completely specify the configuration of the system.

The minimum number of DOF for a fully general spatial manipulator is six: three to control position and three to control orientation. The Cobot-C1, with six joints, is classified as a 6-DOF manipulator.

Cobot-C1's 6 DOF Breakdown:

Joint 1 (Base/Shoulder): Rotation about base axis, enabling horizontal sweep
Joint 2 (Shoulder): Elevation or lowering of the entire arm in vertical plane
Joint 3 (Elbow): Further movement in vertical plane, extending or retracting
Joint 4 (Wrist Pitch): Up/down pitch of the wrist, helping align approach angle
Joint 5 (Wrist Yaw): Twisting the wrist side to side
Joint 6 (Wrist Roll): Rotation about the tool axis for fine-orientation control

Joint Types Comparison

Joint Type	Motion Allowed	DOF per Joint
Revolute (R)	Rotation about axis	1
Prismatic (P)	Translation along axis	1
Spherical (S)	Rotation about all axes	3
Cylindrical (C)	Rotation + translation	2
Universal	Two rotations	2

Denavit-Hartenberg Parameters

Four DH parameters describe the geometry of link i:

a_i (Link length): Distance along x_i from z_i-1 to z_i
α_i (Link twist): Angle around x_i from z_i-1 to z_i
d_i (Link offset): Distance along z_i-1 from O_i-1 to the common normal
θ_i (Joint angle): Angle around z_i-1 from x_i-1 to x_i

Prerequisites

Physical Cobot is powered on and connected to your computer
ROS (Robot Operating System) is installed
The cobo_msgs package is installed and sourced
Python 3 and required packages (numpy, rospy) are installed
Each terminal session must initialize: source /devel/setup.bash

Procedure

Step 1: Positioning by Inputting Coordinates

Navigate to the control script directory:

cd dev/MRL/cobot-C1/src/cobo_control/src/ python3 cobot_joint_angle_reporter.py

Use the c command to move the Cobot:

Enter the desired end-effector pose as six space-separated values: x y z φ θ ψ
Press Enter to execute the movement

Step 2: Record Joint Angles

After the Cobot-C1 moves to the desired position:

Use the r command and press Enter
This prints the current angles of joints 1–6 in both degrees and radians
Record these printed angles for your analysis

Step 3: Positioning by Inputting Joint Angles

Use the j command to move the Cobot by specifying joint angles:

Enter the angles in radians, separated by spaces
Press Enter to execute the movement

Step 4: Repeat

Perform the above steps for several different points to build understanding of kinematic relationships.

Important: Always return the Cobot-C1 to home position before exiting the program using the h command.

Sources of Error and Precautions

Common Sources of Error:

Joint angle measurement errors due to sensor noise

Precautions:

Repeat measurements to minimize random errors
Record environmental conditions that might affect the experiment
Always return the Cobot-C1 to home position before exiting

Learning Outcomes

Grasp the fundamentals of manipulator kinematics
Comprehend the relationship between joint angles, link lengths, and end-effector positions
Recognize the role of joint ranges and link dimensions in shaping the robot workspace
Appreciate sources of discrepancy between theoretical and observed positions
Develop awareness of coordinate and angle conventions in robotics control software