# What is Kinematics equations: Definition and 31 Discussions

Kinematics equations are the constraint equations of a mechanical system such as a robot manipulator that define how input movement at one or more joints specifies the configuration of the device, in order to achieve a task position or end-effector location. Kinematics equations are used to analyze and design articulated systems ranging from four-bar linkages to serial and parallel robots.
Kinematics equations are constraint equations that characterize the geometric configuration of an articulated mechanical system. Therefore, these equations assume the links are rigid and the joints provide pure rotation or translation. Constraint equations of this type are known as holonomic constraints in the study of the dynamics of multi-body systems.

View More On Wikipedia.org
1. ### Ejected out from an accelerating spaceship

Let me copy and paste the problem as it appeared in the text to the right. I start by drawing the diagram of the problem. Scaramanga (drawn as S) gets thrown out with a speed ##v_0## at time ##t_1=3\;\text{s}## from the helicopter which is accelerating at ##a\;\text{m/s}^2## starting from...
2. ### Free fall kinematics problem

I am super stumped at this question, the answer key is telling me 6.78 downwards, i think I'm reading and observing the question wrong. Isn't final velocity 0 so why can't i do 0 = v0 -9.8(0.25) -2.45 = v0 But when I use the second the equation -2 (displacement of door) = v0(0.25) + 1/2...
3. ### Calculating Total Flight Time for a Rocket: A Scientific Approach

I calculated the time for the velocity before ground impact, which is v = -189.23 and the velocity at end of engine burn time, which is 120.996. I also calculated the max altitude (y = 1826.94), and the time to reach the max altitude was t = 23.0823 seconds. So from this information, I did: t =...
4. ### Kinematics equations: Prove that a=vdv/ds

We know that v=v(x, t) i.e. V is a function of time as well as space coordinate here I have only taken 1D motion for simplicity. By chain rule a=dv/dt= Dv/Dx*dx/dt +Dv/Dt*dt/dt where D /Dx represent partial differentiation along x coordinate. So, a=Dv/Dx*dx/dt +Dv/Dt Here we say that Dv/Dt=0...
5. ### Understanding the 1-D Kinematics Equations

So, the equations I'm talking about are the "big 4" listed here: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations I understand how to derive all these using calculus or algebra and graphs. That's not my problem. I can apply them pretty well to problems I need to...
6. ### Kinematics: Two engines, One Rocket, and Displacement.

Homework Statement A Rocket with an engine that causes a net acceleration of 4m/s^2 launches with an initial velocity of 20m/s. The engine fuel lasts for 0.8s. A secondary engine then fires causing a net acceleration of 2m/s^2 for 0.6s How far off the ground is the rocket when the secondary...
7. M

### Whether constant acceleration and zero acceleration are the same

In the equation v=u+at, u=5 m/sec and a=0, then v=5 m/sec. That means the body is moving with a constant velocity of 5 m/sec. In a velocity-time graph, the equation produces a straight horizontal line. Some texts say the body is moving with zero acceleration and others say it is moving with...
8. ### Kinematics Equations: When to Use Each?

I would greatly appreciate it if someone can clarify the conditions on when to use to each of the kinematics equations, because I end up with the wrong answer for using the wrong equations of the 3. 1. vf = vi + at When can I use this and when cannot? 2. vf^2 = vi^2 + 2a(xf-xi) When can I use...
9. ### Auto track using Kinematic model

Hi, I'm trying to implement an auto track guidance system for ground vehicles (Eg Tractors), I'm using Matlab and Simulink. I'm at a point where I can calculate heading errors. I'm not too sure how to calculate the lateral errors. Also, I need help in designing the controller. I'm using...
10. ### Impulse of force correct here?

Im sure Imma mess this up, probably because I am really tired...but I have a bullet that weights .015kg's and is moving at 285m/s, so 609.18J's as with KE. I hit a 70kg block, penetrates .3048 meters thus exerting 1998.62N's of force, which is a lot of force. .3048/285m/s so 0.00106 seconds...
11. ### What is causing confusion in solving for projectile motion?

Hello, I am a first year science teacher doing my best with teaching physics for the first time (my degree is chemistry but I am in a very small school). I am teaching projectile motion. I was creating a worksheet and trying to solve a problem I made up when I realized something wasn't working...
12. ### Solve Trigonometric Problem for Dynamics: 4th Hint Equation

This problem is same as the problem on this link https://www.physicsforums.com/threads/trigonometric-problem.76696/ . I would like to ask the number 4 hint which is "4) We therefore have, for example the equality: " the equations can't be seen on my pc as it will only outputs this...
13. ### Distance traveled with acceleration & deceleration

Homework Statement A man bungee jumps off a cliff and free falls for 3 seconds. The bungee cord stops the jumper in 5 seconds. How far did the man fall in total?Homework Equations X = V0t + 1/2at2 The Attempt at a Solution Xf = X1 + X2 X1 = V1it1 + 1/2a1t12 X1 = 0 * 3 + 1/2 * -9.8 * 32 X1 =...
14. ### Calculate force of friction on car as it rolls across

Homework Statement Calculate the force of friction on a toy car as it rolls across a flat floor. Given: mass = 0.293kg time = 3.66 s displacement = 8.7Homework Equations Fnet = mass x acceleration displacement = [(velocity1 + velocity2)/2] time velocity2 = velocity1 + acceleration(time)The...
15. ### How many equations for kinematics?

This is a small question about the actual number of kinematic equations. I've seen many websites derive 4 different equations, but some only use 3. The 4th equation that I have yet to see be put to use is xfinal=xinitial+1/2(vinitial+vfinal)(time) Could someone explain why some do not mention...
16. ### Kinematics Equations and a Cliff

Homework Statement A car drives off a cliff that is 100m high. It has to land in water and the water starts 30m away from the cliff. Its goal is to land 90m into the water. How fast must the car be going to land at that point in the water. Air resistance is negligible. v=0 v0=? a= -9.91m/s2...
17. ### Dynamics class w/o kinematics equations?

Homework Statement My problem is I don't understand what my professor wants us to do instead. He says that we don't need to memorize any equations, namely the equations of motion, and that everything can be solved with basic principles and integration. The problem is, I have no idea how to...
18. ### Is there some sort of calculus relationship between these two kinematics equations?

{ y }_{ f }={ y }_{ i }+{ v }_{ yi }t+\frac { 1 }{ 2 } { a }_{ y }{ t }^{ 2 }\\ { v }_{ yf }={ v }_{ yi }+{ a }_{ y }t It almost looks like the second equation is the derivative of the first equation with respect to time.
19. ### Confused kinematics equations & ball motion in the air

you throw a ball straight up in the air with a speed of 7.25m/s. The moment the ball leaves your hand you start running away at a speed of 2.59m/s. How far are you from the ball the moment it hits the ground. So I've gotten better at these kinematics equations but this one has too many...

Homework Statement my friend is standing on the roof of my house trying to fix the satellite. Suppose he needs a wrench and asked me to toss one up to him. If i stand 20.0m away and toss the wrench to the top of the 10.0m tall building, what is the magnitude of the velocity with which I need...
21. ### 1-D Kinematics Equations involving time & distance

Hey, I've been working on this problem for quite a while now, and I can't seem to come up with the solution. I would love some help in the right direction. Homework Statement Someone spots a flowerpot that sails first up and then down past an open window. The pot was in view for a total of...
22. ### Calculating Time for a Stone to Hit the Ground from a 100m Cliff

Homework Statement 30. A stone is thrown horizontally from a 100 m high cliff with an initial speed of 10.0 m/s. How long does it take to hit the ground?*  A.* 14.5 s  B.* 4.52 s  C.* 10.2 s  D.* 6.27 s E. 19.2 s Homework Equations The 4...
23. ### Motion in one dimension, Kinematics equations

Homework Statement Two spacecraft are 13,500m apart and moving directly toward each other. The first spacecraft has in initial velocity of 525 m/s and accelerates at a constant -15.5 m/s^2. They want to dock, which means they have to arrive at the same position at the same time with...
24. ### Where Can I Find Help Understanding Kinematics Equations for Pelican Diving?

Homework Statement Pelicans tuck their winds and free fall straight down when diving for fish. Suppose a pelican starts its dive form a height of 20.0 m and cannot change its path once commited (uniform motion). If it takes a fish 0.1 s to perform evasive action, at what min height must it...
25. ### Deriving Kinematics Equations

The Problem: Using V2x=V1x+ax(deltat)t and (delta)x=V1x(delta)t + 1/2ax(delta)t^2 derive the formula V2x^2=V1x^2+2ax(delta)t Homework Equations 1st and 3rd x-component Kinematics Equations The Attempt at a Solution Ok, so I attempted to solve it, but it didn't work. I don't want...
26. ### Kinematics equations with collision fo 2 balls

Homework Statement a ball is shot straight up from the ground with speed Vo. simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest at what height above the ground do the balls collide?asnwer should be a symbolic expression in terms of Vo and g...
27. ### Kinematics Equations (2 Problems)

Homework Statement In solving a kinematic equation for x, which has a negative acceleration, is x necessarily negative? A classmate states that a negative acceleration always means that a moving object decelerating. Is this statement true? Explain. Homework Equations The Attempt...
28. ### Help with kinematics equations (d = v t and the projectile one)

hi, 1. i would like to ask a physics question concerning two basic kinematics equations: d = v t and the projectile equation d = v t + 1/2 a t(squared). i was wondering on how exactly one would take these two equations and (using ONLY the symbols) prove that they should be equal. what i mean...
29. ### Basic kinematics equations question

hi, i would like to ask a physics question concerning two basic kinematics equations: d = v t and the projectile equation d = v t + 1/2 a t(squared). i was wondering on how exactly one would take these two equations and (using ONLY the symbols) prove that they should be equal. what i mean...
30. ### Kinematics Equations: Solve for Stone's Velocity & Time

Hi. Could someone please help me with the following M1 level Maths question. I would really appreciate any help as I am pretty stuck at the moment. A stone is catapulted vertically upwards with a velocity of 25 m/s from a point 2 m above the ground. Find (a) its velocity when it hits the...
31. ### Problems with kinematics equations

I have a few homework questions involving some kinematics equations, vectors, etc. I was hoping I could some help with them. My first question: An arrow strikes a target in an archery tournament. The arrow undergoes an average acceleration of 1.37 x 10^3 m/s^2 [W] in 3.12 x 10^-2 s, then...