HW1: Exploring DOFs and Joint Types in the PincherX 100 Robot Arm plus DOFs Practice Questions - madibabaiasl/kinematics-robotic-arms-modern-approach GitHub Wiki

Learning Objectives

Identify and classify the joint types in the PincherX 100 robot arm.
Apply Grübler’s formula to compute the robot’s total degrees of freedom (DOFs).
Experimentally verify the calculated DOFs through Python-ROS control in both simulation and the physical robot.
Extend the analysis to complex systems such as Boston Dynamics’ Spot and its robotic arm.

Learning Outcomes

After completing this homework, you will be able to:

Describe how different joint types constrain a robot’s motion.
Demonstrate an understanding of how theoretical DOF calculations translate into real robot movement.

Why This Matters

This assignment puts the degrees of freedom (DOF) theory from Lesson 2 into motion. By identifying the PincherX 100’s joints and applying Grübler’s formula, you will connect mathematics to real robotic behavior, seeing how each joint adds or limits motion. Extending the same logic to Spot’s legs and arm shows how the same DOF principles govern both manipulators and walking robots.

PincherX 100 Robot Arm DOFs and Joint Types

Equipment:

PincherX 100 Robot Arm
Computer with PincherX control software installed

Step 1. Identify the joint types in the PincherX 100 robot arm and discuss how they constrain the movement of the links (15 points).

Step 2. Using Grübler’s formula that we learned in lesson 2, calculate the total DOFs of the PincherX 100 Robot Arm (do not take into account the opening and closing of the end-effector). Note that a joint connects two links and traditionally ground is considered a link (because the first joint connects the ground to the first link of the robot) (15 points).

Step 3. Using the joint control code we had in one of the class activities, experimentally show that the robot actually has that number of DOFs. Write the code and first show it in simulation and then try it on the robot arm. Submit a video for this part (15 points).

Practice Exercises

Spot is an agile mobile robot designed by Boston Dynamics to help automate tasks that are either dangerous or tedious for humans to do. It is mostly intended to be used in construction sites, contaminated environments, power plants, and other areas. It consists of a main body with four legs, and can also have a robot arm to increase its versatility. The robot arm enables Spot to navigate harsh environments and interact with the world in various ways, such as opening doors, flipping breakers, and carrying small loads. Spot, together with its arm, can be seen in the following figures:

spot_boston_dyn

Spot quadruped robot with arm from Boston Dynamics.

For your attention, I have shown joints and links in one leg as follows:

spot_robot

Joints and links of one leg of spot.

The same can be applied to other legs. Use Grubler's formula to find the degrees of freedom of the Spot robot (20 points).

A diagram of the Spot's arm (Courtesy of Boston Dynamics) is shown in the photo below. Find the degrees of freedom of the arm using Grubler's formula (20 points):

spot_arm

Spot's arm (Courtesy of Boston Dynamics).

Report Requirements for Homework 1

Submit reports individually.
Title, Name (5 points)
Meeting the requirements of each part or question above that has points in front of it.
Reflection: A short reflection on any interesting observations, surprises, difficulties, new directions that can be taken and any other feedback you may have (5 points).
References: Note that utilizing (or not utilizing) AI should be disclosed here. You can use AI according to the allowed instances in the Syllabus. Also, 100% AI-generated content will get 0 (5 points).
The codes can be submitted through a GitHub repo (with link provided) or alternatively be uploaded to/included in the submission.

Note: This activity is eligible for "best report" and "best video" points in our reward system (see the reward system sheet for the criteria).