# Questions tagged [screw-theory]

A method of representing the mechanics (kinematics and dynamics) of a system using 6-element vectors (such as a twist or a wrench) which combine both the angular and linear components.

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### Adding an Actuator or Force to a (Featherstone) Articulated Rigid Body Model

I'm working on a project where I need to model a system that is essentially comprised of a series of ball-and-socket joints attached to a base, which is attached in turn to a prismatic joint (rail). ...
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### How is Screw Theory used in Robotics when you can do everything with regular kinematics?

I was seeing some Robotics lectures and a word which keeps coming up is "Screw Theory", on looking it up, I find that everything you can do with it practically, you can do with vector ...
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### Relationship between the velocity twist Jacobian and the spatial velocity Jacobian

While reading Kevin Lynch's "Modern Robotics" [1], I came across a fundamental question concerning the manipulator Jacobian. Upon better reading and further cross-checking with Peter Corke's "Robotics,...
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### The Jacobian resulted from Screw method is different from analytical one (Example Inside)

I am currently solving a kinematics example that asks for the Jacobian. However, when I solve it using the Screw method I get different results from the analytical method, The example is kinda hard to ...
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### question about spatial velocity in the book <modern robotics>

I think the equation(3.73) should be: $\dot p-w_s$x$p=\dot p-\dot p=0$ have no idea how it can be wrong and don't know the difference between infinitely large body and a body just include the fix-...
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### What is the difference between screw and wrench in rigid body motion?

A screw is defined by a six dimensional vector of forces and torques. It can represent any spatial movement of a rigid body (as written here). But I don't get the following distinction between screw ...
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### Stationary/inertial reference frame

In Modern Robotics by Kevin Lynch, there is a term "stationary" frame, but this is never defined. Googling shows that this is synonymous with inertial frame. Apparently inertial frame means ...
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### Robotic manipulator Jacobian by product of exponentials

I've taken a class and started a thesis on robotics and my reference for calculating the Jacobian by product of exponentials seems incorrect, see: http://www.cds.caltech.edu/~murray/books/MLS/pdf/...
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### Velocity description in Screw Motion Theory

As described in the book Modern Robotics by Frank C. Park the velocity of a reference frame can be described as : $$V_s = J_s(\theta)\dot{\theta}$$ $$V_b = J_b(\theta)\dot{\theta}$$ However in the ...
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### Articulated Body Algorithm with gear ratio

I am reading up on the proposed articulated body algorithm by Featherstone, which goes like: Pass 1: \nu_0 = 0\\ \nu_i = {^i}X_{\lambda(i)}\nu_{\lambda(i)}+s_i\dot{q}_i\\ c_i = \nu_i \...
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### Forward kinematics confusing point

I am studying robot arm kinematics. In order to construct a transformation from a global coordinate frame to the end effector frame, I have seen references to the Denavit–Hartenberg (DH) convention. ...
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### Difference between Denavit-Hartenberg and Rodrigues formulas/conventions

I am trying to compute the forward kinematics for a 6 DOF robot arm. I've found two methods : the Denavit-Hartenberg (original and modified) and the product of exponentials with the Rodrigues formula. ...
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### Kinematics with Product-of-Exponentials terminology: not forward, not inverse

I'm working on a kinematic estimation algorithm, and am trying to come up with the right terminology. I'm using the Product-of-Exponentials formulation for kinematic chains (and ignoring position ...
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### Screw based Jacobian

I am working on kinematics of 5-DOF robot. I already derived geometric Jacobian for position and orientation control. But for singularity analysis, I require a simplified jacobian. And that can be ...
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### Explanation for exponential coordinate of rotation

From figure above, suppose a three-dimensional vector $p(0)$ is rotated by an angle $\theta$ about the fixed rotation axis $\omega$ to $p(\theta)$. Here we assume all quantities are expressed fixed ...
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### How to get the 4*4 matrix from the twist using product of exponentials, in robot kinematics?

In robot kinematics, we have $e^{(\theta*twist)}$, where $twist$ is 6*1 vector. How do I get the 4 by 4 transformation matrix by using product of exponentials?
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### How do you calculate this integral term in this PI Controller Formula?

This formula is the PI Control given in Eqn. 11.6, Pg. 419 of Chapter 11 in book Modern Robotics by Kevin M Lynch and Frank C Park. Here, Vb is the twist ==> Vb = (angular velocity, linear ...
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### Free-floating sphere dynamics using Roy Featherstone's spatial_v2 toolbox

I am using Roy Featherstone's spatial_v2 to model a mobile robot. I encountered a problem so I went back to modeling a free-floating sphere to familiarize myself with the library and the algorithms. ...
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### How to find the body jacobain, for each link in a robot manipulator?

The links twist could be obtained, and thus The spatial manipulator Jacobian could be done, but when it comes to the body Jacobian, it is becomes difficult. Moreover, the adjoint transformation ...
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### 3D Rigid Body Pose Optimization in flat euclidean space

I am confused about what is the best way to optimize the 3D pose of an object and the best way to parametrize the translation and rotation for optimization in flat euclidean space. Assume I have a ...
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### Understanding Twists as 3D Velocities

I am just learning about twists to represent 3D velocities (e.g. of a robot's end-effector), and I have two questions: 1) Wikipedia defines a twist as "an angular velocity around an axis and a linear ...
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### Screw Axes in the Base Frame

I'm trying to find screw axes for joint (on pic) with angle θ. It's on zero position. As I understood: joint has an angular velocity on the Z axis, clockwise, so the sign is positive and ω=(0,0,1); ...
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### v_s quantity in twists

In Modern Robotics v2, we have the following figures: I don't understand why in Eq. 3.73, we have the given expression for $v_s$. My thinking is: The position $p$ is the position of the frame $b$ ...
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### perplexity about ch8.2.1 the linear dynamics, in the book <modern robotics>

From previous chapters, I think I have understand the twist, it is about the angular velocity and the linear velocity, the difference is that linear velocity is not one fixed point in the body but is ...
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### How to calculate twist and wrench in local and global frames [closed]

I am rather new to screw theory and also lost in robotics books' formulas. we have a simulator of a robot arm within Mujoco physics engine and I'm wondering how I can calculate wrench and twist in the ...
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### theory on rigid body motion in robotics book

I am reading some theories related to rigid body motion from the book "A Mathematical Introduction to Robotic Manipulation" by Prof. Richard Murray. I am focusing on chapter 2, Sec 4 to derive some ...
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### Libraries to calculate kinematics using Screw Theory

Most kinematics libraries/packages use the conventional transformation matrices (DH parameters). However, I'm looking for something that uses Screw Theory principles to set up the Product of ...
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### Newton-Euler Inverse Dynamics by Screw

I paste this algorithm from textbook Modern Robotics P294 in chapter 8: This is coordinate invariance of Newton-Euler equations. In the textbook, they use the ...
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### A single screw axis of a rolling wheel - seems impossible...?

Chasles' theorem: "Any rigid-body motion can be specified by a rotation about a screw axis and a translation parallel to that axis." For a rolling wheel, the axis of rotation is ...
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### Screw theory for kinematics/dynamics of mechanisms

Is screw theory commonly used for general kinematics/dynamics of mechanisms (not just robotics)? I'd be interested in anything that covers the types of mechanisms you would find in a typical ...
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### Relationship between Lie Algebra (Murray, Lynch) and spatial vector (Featherstone) approaches

I am curious about the relationship between the Lie algebra/group approach to robot kinematics given by Murray (et al.) in "An Introduction to Mathematical Robotic Manipulation" and Lynch (...
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### Adjoint representation of twists in the Jacobian derivation

In section 5.1.1 of Modern Robotics by Park and Lynch (pg. 153 of 1st edition, pg. 177 of updated 1st edition), the following derivation is given for the Jacobian matrix. I don't understand this ...
A frame {b} is attached to the centre of a robot chassis. The planar configuration is given by $(x,y,\phi)$ where $\phi$ is the angle between the x axis in {b} and the x axis of a fixed reference ...
This is a homework question from edx course Robot Mechanics and Control, Part II Given the following and expressing its forward kinematics as $T = e^{[S_1]\theta_1} ... e^{[S_6]\theta_6}M$ It is ...