# Questions tagged [kinematics]

Kinematics is the branch of mechanics dealing with the motion of points and objects.

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### How can I find the kinematics 2 differential drives attached together along their axes?

I have a system like shown in the diagram where 2 robots having differential drive are physically constrained together. Traditionally for a single robot, we find the Instantaneous center of curvature (...
85 views

### How to calculate potential enegy of manipulator dynamics?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is two main things one is kinetic energy and the other ...
51 views

### Cartesian control for $z$ vector of end effector frame to point towards a specific direction

Consider a robotic manipulator with 7-DOF (all joints are revolute) that accepts joint velocities as execution commands. What I am trying to achieve is the following: I want to calculate the ...
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### Problem designing acceleration inputs controller

I am reading this paper: https://www.researchgate.net/publication/224635390_The_motion_control_problem_for_the_CyberCarpet in which is implemented a cartesian regulator to bring the position $(x,y)$ ...
84 views

### How to calculate potential enegy of manipulator?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is two main things one is kinetic energy and the other ...
81 views

### How to calculate Inertia tensor?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is a term I - Inertia tensor . I couldn't understand the ...
94 views

### Forward Kinematics for Two Axis Gimbal Mount

I'm trying to work out the orientation of a block at the end of two axis gimbal. I know the position of the two rotational joints, but would like to calculate the final orientation of the block given ...
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### C space for R5 manipulator

Trying to create a collision avoidance model (RRT) for an RRRRR manipulator. I am unable to wrap my head around how to represent the same in configuration space. Anything upto 3 joint variables is ...
38 views

### How can I find a robot's distance from an object given FOV, bounding box measure, and image width and height in pixels?

The robot is standing in the middle of the arena. I am confused on how to convert the pixels into a real life distance and how to use the bounding box. Starting help is appreciated.
208 views

### Multi-Link Robot Degrees of Freedom

I want to compute the DOF of this system if it composed of (n) such links grasping this common object using Grubler's formula obtaining the solution as a function of (n), considering this to be a ...
123 views

### Compute orientation velocities 6-DOF robot

I am trying to compute the joint velocities a 6-DOF manipulator(a typical industrial robot). I have an initial position [xi, yi, zi, T1i, T2i, T3i] and goal position [xf, yf, zf, T1f, T2f, T3f] in the ...
162 views

### Chebychev–Grübler–Kutzbach Formula of Degree of Freedom

I always have had a problem understanding Chebychev–Grübler–Kutzbach Formula of Degree of Freedom: $$d = 6\,n - \sum_{i= 1}^{m}\left( 6 - f_i\right)$$ where $n$ is the number of moving links, $m$ is ...
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### How to do a relative rotation of a cuboid such that the longest edge is upright?

I am using pybullet. I have a cuboid with half extents [4,2,1] corresponding to x,y,z dimensions. I rotate this cuboid around the z world axis theta and also translate it by [0, 0, .65]. I take a ...
178 views

### Cartesian Velocity Control between Two 3D Poses

I am really struggling to understand how to do Cartesian velocity control when 3D rotations are involved. So, below is a very simple example which I am hoping somebody can help me with. Let's say the ...
61 views

### How to find inertia parameter of payload automatically

I know of several robot manufacturers who can perform automatic inertial measurement for 6 axis robots. Fanuc, for example, moves with axes 5 and 6 each from +180 to -180 °, once with and once without ...
157 views

### Cartesian Angular Velocity

Let's say I have a Jacobian which gives the relationship between the velocity of a robot's joints, and the Cartesian velocity of its end-effector, relative to the end-effector's local frame. And let's ...
57 views

### Design optimization method using indices

There are several methods like manipulability and conditioning index for design optimization kinematics performance, but these methods rely on the singular values of the jacobian matrix. I described ...
65 views

### Dexterity calculation with dual quaternions

How can the manipulability of a robot arm be calculated when the kinematics are described with screw theory such as dual quaternions? These methods are sigularity-free, but what could we say about ...
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### Difference between constant curvature kinematics and rigid link kinematics

What is the difference between constant curvature kinematics and rigid link kinematics and what is their respective definition?
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### Jacobian to determine the linear velocity of each node (DOF 3 RRR robot arm)

I've done the FK and IK for this robot: On those I seem to be able to get to the positions I want on the simulator so I'm assuming nothing is wrong with my FK and IK calculations. I've tried to ...
164 views

### Inverse Kinematics with Orientations

Let's say I have a robot consisting of a base $B$ and a manipulator $M$. The pose of the manipulator can be expressed as the transformation matrix $T_{BM}$. I also have a goal $G$ which I want to move ...
53 views

### From an end-effector trajectory to joints movements

let's assume that our robot consists of 3 degree-of-freedoms. In order to move the end-effector of this robot along a straight line, these 3 joints have moved as below: Now, if the desired end-...
245 views

### SLERP velocity and acceleration (3d Orientation interpolation)

Hey guys I am quite new to quaternions and I am a bit unsure as to how to use them. How are the velocities and accelerations trajectories determined using quaternions? I have been using slerp to ...
80 views

### 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 ...
41 views

### How to represent the Xf axis of the final frame (end-effector) in function of euler angles?

I am working on a robot arm with 7 rotational joints. I can generate the T of any position, what I want to do ist to represent the vector Xf of the end effector frame in the base frame. How can I do ...
63 views

### Degree of maneuverability mobile robot

According to the traditional kinematic theory for mobile robots  a mobile robot with a steerable wheel and two passive casters presents a $\delta_m=2,\delta_s=1,\delta_M=3$. This is easy to ...
530 views

### Why with the pseudo-inverse it is possible to invert the Jacobian matrix even in a singular configuration?

Consider the following situation: I have a robotic arm manipulator with all revolute joints, for example consider a 2R planar manipulator. We know that if we compute the direct kinematics of it, anf ...
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### How do I compute the derivative of the Jacobian with Matlab?

I am studying robotics, and I am trying to write a Matlab code for computing the derivative of the jacobian matrix. The formula for computing the derivative of the Jacobian is the following: so it ...
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### Self motion with multiple constraints

I am trying to control a 7 DOF robot (a Franka Panda). I use jacobian based control (resolved rate motion control) to generate a joint trajectory from a cartesian trajectory. My contraints for the ...
66 views

### motion model for forward movement

I thought this is a simple and well known problem and therefore there is a lot of literature. But I'm not able to find the correct keywords to google the answer. Maybe instead of answering the whole ...
34 views

### Link collision avoidance for redundant manipulator

I am trying to have my robot arm follow a trajectory while avoiding collisions between obstacles and the robot links. The way I go about it is to find the closest point on the robot arm, and treat the ...
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### I want to Calculate the Joint Velocities and Angular Accelerations of 5 DOF Youbot kuka robotic arm

I'm working on an assignment where I need to derive Velocity Kinematics for 5 DOF Youbot kuka robotic arm manipulator. I want to Calculate the Joint Velocities and Angular Accelerations of 5 DOF ...
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### Finding quaternion Q, where Y = q * X * q.inv()

Problem Quaternions $X$, $Y$, which represents 3-dimensional points are given. Quaternion $q$ is what is to be solved. I want to know unknown rotation between $X$ and $Y$. In other words, I want to ...
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### Can someone help me understanding reference frames in OxTS data in KITTI Vision Benchmark dataset?

If anyone has worked with KITTI dataset, can you explain the reference frame used in roll pitch yaw values? I downloaded the raw data from this link: http://www.cvlibs.net/datasets/kitti/raw_data.php ...
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### Formulas for calculating the passive joints angular velocities

We have the following parallel robot architecture: Positions of the vectors $u_i, v_i, w_i$, the angles $\theta_i$, angular velocity $\dot{\theta_i}$ and the Jacobian $J$, that mapping vector of ...
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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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### How do I get the matrix for the mass?

Hi im currently studying for an introduction on robotics test and i have this task to calculate the kinetic and potential energy of the robot. The robot is an open chain and has one rotating joint as ...
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### Controlling a robot arm to follow an SE(3) trajectory

I have a 7-DOF robot arm, and I want it to follow a trajectory. This trajectory is defined as a dense sequence of SE(3) waypoints, which were collected by moving the robot arm manually (i.e. by ...