Questions tagged [kinematics]

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How to show that the total angular velocity vector of a rigid body is the sum of all angular velocity vectors acting on it

I am trying to prove the additivity propety for the angular velocity vectors acting on a body in three dimensions. Particularly also in the case when the axes of rotation do not cross each other (the ...
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19 views

Relation between links and pairs in Kinematic chain

I came across a equation for kinematic chain (for lower pairs only) : L = 2P-4 where L: Number of Links; P is the number of pairs how could this equation be derived ?
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34 views

Linearisation of the Equations of Motion of an Inverted Double Pendulum

I am working to develop a deep reinforcement learning model for balancing an inverted double pendulum. To do so, I needed to derive the equations of motion, via the Euler-Lagrange (EL) method and now ...
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17 views

Sprocket Angular Velocity [duplicate]

I have a question please that I need help on. Consider the chain that is draped over the sprocket with mass moment of inertia of 0.005kgm^2 about central axis. If 4kg block is released from rest from ...
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1answer
64 views

To stop or to go around?

Let us we are moving in a car. There is a wall in front of us, we need to decide can we go around it or not. It is known that width of the wall is $w$ and our speed is $v = const$. What is a simple ...
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101 views

Degrees of Freedom for Complex Pulley Systems

I'm trying to understand DOF clearly, but this pulley system has me doubting myself. When I try to determine the degrees of freedom, I sum the DOF of each object, and subtract the constraints. for ...
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3answers
58 views

In circular motion , why do we say this is centripetal acceleration

Let us say a particle is moving in a circle with Uniform circular motion . Then , if I take an equation like this . $\theta$ = S(Arc length or Total distance covered ) / Radius of circle *( time ...
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36 views

Did not understand this regarding angular velocity

It says $V\sin \alpha$ (component of velocity perpendicular to OP) is the cause of angular displacement. How is it? if only $V\cos \alpha$ existed, we need not turn over head to always to look at a ...
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1answer
46 views

Gear Ratio of a Stepped Planetary Gearset

I was looking into planetary gearsets, and came upon the concept of a stepped planetary gearset. In the image shown above, if my input was the blue sun gear, the output was the planet gear, and the ...
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11 views

3DOF end effector control

I have created a simple serial robot with some servos and CAD. Each joint has 180 degrees of freedom, where they all have 180 degrees of freedom. I haven't specified where the 180 degrees of freedom ...
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1answer
24 views

differential drive vehicle in screen coords

differential drive vehicle in world frame what would change in the kinematic model of the differential drive vehicle if i wanted to simulate it using pygame module in python ( pygame or opencv or any ...
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25 views

Problem in the inverse kinematic model of a car like vehicle?

I'm a electrical engineering student and i am building a simulation of a car like vehicle . As I understand it: The input for the forward kinematic model are the control variables and the output is ...
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56 views

What does it mean for a machine design to be “kinematic”?

I've seen the term "kinematic" used qualitatively to describe machines several times in books and on YouTube. I think I understand what kinematics is as a study, but I'm not sure what people ...
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32 views

Stewart platform 6DOF parrallel manipulator static force diagram

I am trying to develop a statics free body diagram of a stewart platform 6dof parallel manipulator motion table. I have the base points (B1,B2,B3,B4,B5,B6) and the top platform points (P1,P2,P3,P4,P5,...
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91 views

What do I need to operate this motor?

I am currently designing a tennis ball launcher. I am looking to use the friction wheel approach, where you have the ball passing through 2 spinning wheels and being launched by the frictional force. ...
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1answer
30 views

Euler rotations and acceleration

I have a system determined by 3 Euler angles that describe the orientation with respect to a fixed coordinate system XYZ. The angular velocioties are: $\omega_2$ (precession), $\omega_1$ (nutation) ...
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25 views

How to measure / calculate Tait-Bryan angles of a moving platform in SimMechanics

I exported a model of the mechanism created in SolidWorks to SimMechanics in order to explore the possibilities of control. To solve the problem, i need to know the angular position of the mobile ...
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1answer
36 views

Maximum velocity of an athlete [closed]

I was solving a mechanics sum An athlete running a 100m run starts from rest and reaches the maximum speed in a distance of 15 m. He runs the remaining distance with that velocity and reaches the ...
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1answer
19 views

Purpose of normalization of Jacobian in a parallel manipulator

I am currently studying a robotics paper, where a normalized frobenius norm of a matrix is calculated as part of determining the condition number of the corresponding linear system of equation: $\...
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1answer
33 views

I have the yaw rate, rear wheel speeds, and the radius of tires, how to find x and y speeds?

I only have these 3 data sets: rear right and left wheel speeds (they change with time) yaw rate (also changes with time) constant dynamic rolling radius How am I supposed to find the directional ...
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1answer
96 views

Center of rotation (rigid body)

I know the meaning of (instantaneous) “center of rotation” and “center of zero acceleration” for a rigid body. I know that they do not coincide (in general) and that their positions change with the ...
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1answer
83 views

How to compute the size of a polygon moving along non-circular guide rails

I am trying to compute the optimal (a non-optimal solution would also work) size of carts that can move along guiding rails. Each cart is connected to the rails at two points. Each cart is also ...
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1answer
51 views

How do I call a kinematic assembly that converts rotary motion to sawtooth linear?

I have in mind a device somewhere in between a firearms trigger and a clock escapement. One way it could be constructed is as follows: A crank would displace a linearly moving slider backwards, so ...
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1answer
773 views

What are displacement field and Deformation field?

I am studying mechanics of materials while I came across these terms called the displacement fields and the deformation fields. I am not able to understand the difference between them. Can someone ...
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1answer
205 views

Designing cylindrical cam

So I need to design a cylindrical cam (aka barrel cam I think). I'm an aerospace engineer so I've never had a course on cams/gear design (wish I had though). Is there a general equation for the curve (...
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1answer
115 views

Moment of Inertia of a Rotor System

I need to settle a discussion on the following question: Part A: Find the equivalent spring constant for springs in series Use equations of motion, sum of torques to find natural frequency of the ...
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1answer
44 views

Torque computation for different attachment point

I have a pretty basic question but I would like to be sure of what I think. I have a setup like the one in the figure. I have two motors which can generate two forces $F_1$ and $F_2$ perpendicular ...
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99 views

Dynamics of a rigid body in a system of two linear drives

I've been trying to solve the dynamics of this system for quite a while, but cannot seem to get the right answer. I've tried solving it with Lagrangian method but I am not so confident with the ...
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1answer
530 views

Deriving the equations of motion for free-floating spacecraft with a single link robot arm

Note: I had previously posted this question on the Space and Robotics SE sites, but received little/no response. So I've deleted the previous posts and repasted my question here in the hope of ...
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1answer
284 views

Inertia relief in ANSYS - rotating model

I'm trying to use ANSYS to solve statically a dynamic problem. As shown in the image below, there is an orange bar that is constraint to slide horizontally only and attached to another bar (pink) ...
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1k views

How to calculate the coupler length in a crank rocker mechanism

I'm trying to learn a bit about building kinematic mechanisms by building a small project. The goal is to be able to open and close a box programmatically via a servo motor. I have a small box that ...
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1answer
396 views

4 Gears in a Circular Pattern - Calculating the Proper Distances for Meshing

I have recently been working on a gearbox for a robot. I have this pattern of 4 gears with each gear connected to its 2 neighbors. It looks like this: You will probably notice something though. ...
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1answer
107 views

Bending Moment Doubt

I don't understand how bending moment is being calculated in the problem mentioned in the above link. I understand the parts after that i.e. calculating elastic potential and partial derivatives but I ...
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2k views

What is meant by “shock load” in gears?

What is meant by shock load in gears? What are steady, light, medium and heavy shock loads?
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49 views

No. Of Instantaneous centres

I’m reading “Theory of Machines and Mechanisms” by Joseph Shigley. Page No. 118 - The author states that A mechanism has as many instant centres as there are ways of pairing the link numbers. Thus,...
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Rotating four cylinders with one motor/actuator

I have a setup with 4 cylinders placed next to each other in following configuration. The cylinders are made of .2mm stainless steel. I would ideally want to rotate them along their axis using a ...
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1answer
74 views

Unachievable motions because of singular Jacobian

This is the Jacobian of a robot arm (IBB IRB 120) with already specified joint angles (0,0,0,0,0,0). This Jacobian is singular for this configuration. ...
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333 views

Inverse kinematics solutions pros and cons

I know at least 3 different approaches to solve inverse kinematics problem. They are pseudo inverse jacobian, cyclic coordinate descent and ANFIS networks. I would like to know advantages and ...
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3answers
154 views

Compound gear system: Finding velocity

In the figure below we have that the gear $A$ is has an fixed axis and has the radius of $R_a = 0,1m$ and, in the instant represented in the figure spins clock-wise with angular velocity $\omega_a = 4\...
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183 views

Rotational Motion Kinematics - Not sure how to fix axis of rotation

Hi I am trying to make a CAD model of something like the scoop sampler shown below. http://www.rolls-royce.com/~/media/Files/R/Rolls-Royce/documents/customers/nuclear/scoop-sampling-tcm92-50918.pdf ...
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Forward and Inverse Kinematics of PUMA 560

I am currently coding a Forward and Inverse Kinematics solver for a PUMA 560 robot. For the Inverse Kinematics part I am using the closed for solution given in this paper. But my issue is, my solution ...
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force transmission in kinematic chain

In the following kinematic chain, I would like to get equation to go from $F_{in}$ to $T_{out}$. (excuse the poor drawing, nodes 3,4,5 are always aligned) Here's my attempt : The torque at $1$ is : $...
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215 views

Universal joint vs Double Universal Joint (CV configuration) kinematics

Concerning this subject, I consulted the following Wikipedia page: Universal joint where the elementary kinematics equation of the U-joint is stated. But, a little bit further in the article Double ...
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170 views

Kinematics Mechanics Find the length of the belt and the speed of the rack

For A. I know that the formula for belt is simply $L=\frac{Pi(D_a+D_b)}{2}+2C+\frac{(D_b-D_a)^2}{4C}$ Which gives me $L= 116.99"$ since C is equal to $50$ For B. However I'm stuck and can't get the ...
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Parameter effects on kinetics of esterification for bio-diesel production

I want to discuss the effect of parameters on the kinetics of esterification for bio-diesel production. In esterification process, temperature effect and molar ration are two important parameters. ...
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1answer
960 views

Deformation gradient, strain tensor from cylindrical coordinates

I do not have any engineering background but I am studying some mathematics to try and understand and solve this problem. I have a mesh (M1) in cylindrical coordinates and this deforms into a mesh (M2)...
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2answers
167 views

Questions on machinery terminology

I have some questions in the basics of machinery terminology Can a spring ever be a link? Most books (eg. Ham et al. 58, Shigley pg. 5) consider links to be rigid. However, I have come across ...
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145 views

How to interpete the formula: $I_{G}\alpha = \dot{\vec{H}}$?

I am having hard time to fully undestand what those formula's actually mean. I know the meaning of each element: I : moment of inertia H : angular momentum $\alpha$: angular acceleration $\omega$: ...
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9k views

Calculating torque needed to climb a graded hill

I've been designing an electric skateboard which is driven by only one of the rear wheels (for the moment). As I was picking out motors for the board, I soon realized I would need to find a balance ...
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2answers
442 views

How to calculate the velocity of a piston-like linkage?

I ve tried to solve this problem in so many ways but still didn't manage to do it... What would be the correct way to solve it please? This arm of this mechanism has a length of 0,2m. The piston has ...