[Paper Review] Development of Direct Kinematics and Workspace Representation for Smokie Robot Manipulator & the Barret WAM.

Reza Yazdanpanah Abdolmalaki|arXiv (Cornell University)|Jul 16, 2017

Robotic Mechanisms and Dynamics1 references3 citations

TL;DR

This paper presents a direct kinematics and workspace analysis framework for the 6-DOF Smokie Robot and Barrett WAM manipulator using Denavit-Hartenberg (D-H) parameters and MATLAB-based simulation. By deriving D-H parameters, constructing transformation matrices, and employing the Monte Carlo method for sampling joint configurations, the study generates 3D workspace visualizations, validating results against published WAM data with strong similarity, thus enabling accurate kinematic modeling for both robots with no prior public workspace data for the Smokie Robot.

ABSTRACT

This paper discusses modelling two 6 DOF arm robots. The first step of modelling a robot is establishing its Denavit-Hartenberg parameters. It requires assigning proper coordinates for each link and finding their exact dimensions. In this project we will develop the direct kinematics and workspace representations for two manipulators: the Smokie Robot and the Barrett WAM. After finding the D-H parameters and creating Transformation Matrices,MATLAB programming is used to represent their workspaces.

Motivation & Objective

• To develop accurate direct kinematics models for the 6-DOF Smokie Robot and Barrett WAM manipulator using the Denavit-Hartenberg convention.
• To derive D-H parameters and joint limits for both robots based on physical measurements and design specifications.
• To simulate and visualize the 3D workspace of both robots using MATLAB and the Monte Carlo method.
• To validate the WAM workspace simulation against published data to ensure methodological accuracy.
• To provide a reproducible computational framework for workspace analysis of serial manipulators with no publicly available workspace data, particularly for the Smokie Robot.

Proposed method

• Application of the Denavit-Hartenberg (D-H) convention to assign coordinate frames to each link and determine the four D-H parameters (ai, di, αi, θi) for both robots.
• Construction of homogeneous transformation matrices Ai-1^i using the D-H parameters, with each matrix dependent on the joint variable (θi for revolute joints).
• Use of the Monte Carlo method to sample N = 20,000 random joint angle combinations within specified joint limits to explore the full range of motion.
• Computation of the end-effector position by post-multiplying individual transformation matrices to obtain the final homogeneous transformation matrix T = A1*A2*...*A6 (or A7 for WAM).
• Extraction of the end-effector’s x, y, z coordinates from the fourth column of the final transformation matrix for 3D plotting.
• Visualization of the workspace using MATLAB’s plot3 function with multiple views (isometric, top, side) via the view command, enabling comprehensive spatial analysis.

Experimental results

Research questions

• RQ1 How can the direct kinematics of the Smokie Robot and Barrett WAM be accurately modeled using the Denavit-Hartenberg convention?
• RQ2 What are the D-H parameters and joint limits for the Smokie Robot and the 6-DOF version of the WAM, based on physical measurements?
• RQ3 To what extent does the simulated workspace of the WAM match the manufacturer’s published data, validating the simulation approach?
• RQ4 How can the Monte Carlo method be effectively applied to generate high-resolution 3D workspace representations for serial manipulators?
• RQ5 What is the workspace volume and spatial distribution of the Smokie Robot, given its lack of publicly available kinematic data?

Key findings

• The D-H parameters for the Smokie Robot were successfully derived from physical measurements using calipers and rulers, with joint limits set to ±180° for all six revolute joints.
• The 6-DOF version of the WAM was modeled by fixing the lower arm rotational joint, resulting in a 6-DOF system with joint limits ranging from -4.8 to 1.3 radians for joint 5.
• The Monte Carlo simulation with N = 20,000 samples produced high-resolution 3D workspace visualizations for both robots, including isometric, top, and side views.
• The simulated workspace of the WAM showed strong similarity to the manufacturer’s published data, confirming the validity and accuracy of the simulation framework.
• The Smokie Robot’s workspace was visualized for the first time in this study, as no public workspace data was available from the manufacturer.
• Increasing the number of samples (N) improved workspace resolution but increased computation time, indicating a trade-off between accuracy and efficiency in simulation.