# Trapezoidal motion/kinematics calculations - solving for slewing velocity

• larsbentley
In summary, you are trying to program a motion control device to define a move. You can define the slewing (peak) velocity, accel/decel rates and distance to travel, and the hardware moves a motor the appropriate distance with the parameters given. The move will always be a trapezoid.

#### larsbentley

I am trying to program some motion control devices which have trapezoidal motion profiles to define a move. I can define the slewing(peak) velocity, accel/decel rates and distance to travel, the the hardware moves a motor the appropriate distance with the parameters given.

I need to be able to define a specific amount of time that a move will last, and calculate what the peak velocity should be when all other factors are known. Starting velocity is not always zero, but ending velocity will always zero for my purposes. The move will always be trapezoidal.

I have an equation for defining the distance traveled when all other factors are known, but I need to isolate the peak velocity to one side of the equation and I am not sharp enough at this math to be able to solve for the peak velocity. Any help would be greatly appreciated.

Assuming:
d = total distance traveled
t = total time
AC = acceleration
DC = deceleration
Vi = initial velocity
Vs = slewing (peak) velocity
Vf = final velocity

I have this equation which I believe is correct. I need to isolate Vs to one side:

d = [(Vs+Vi)/2]*[(Vs-Vi)/AC] + [(Vs+Vf)/2]*[(Vf-Fs)/DC] + Vs*[t-((Vf-Vs)/DC)-((Vs-Vi)/AC)]

I hope that's clear enough to read... If not I attached a JPG of the equation written out by hand.

#### Attachments

• KinematicEquation.jpg
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Since Vs appears in two factors of both the first and third terms, that equation is quadratic in Vs. Multiply everything out, determine the coefficients of $V_x^2$ and $V_s$, and use the quadratic formula.

Thanks for that... I'll give it a try. Am I correct that the x in Vx^2 you mentioned is supposed to be an "s" ? It's been a long time since I've done this kind of math so if I'm not entirely sure I'll get this right... if anyone has some more specific tips I'd love to hear them.

Lars

I am having a lot of trouble factoring the equation once I get it in quadratic form, so I can isolate Vs. Can anyone help? If someone can solve this for Vs or give me more help getting started I'd really appreciate it.

Lars

## 1. What is trapezoidal motion in kinematics?

Trapezoidal motion refers to a type of motion where the acceleration and deceleration of an object follows a trapezoidal shape. This means that the object starts moving at a constant velocity, then accelerates until it reaches a maximum velocity, maintains that velocity for a period of time, and then decelerates back to a constant velocity.

## 2. How do you calculate the slewing velocity in trapezoidal motion?

The slewing velocity in trapezoidal motion can be calculated by dividing the total distance traveled by the total time taken. This can be broken down into three steps: calculating the acceleration time, calculating the constant velocity time, and calculating the deceleration time. Once these values are known, they can be plugged into the formula: slewing velocity = distance / (acceleration time + constant velocity time + deceleration time).

## 3. How is trapezoidal motion different from other types of motion?

Trapezoidal motion is different from other types of motion, such as linear or circular motion, because it involves both acceleration and deceleration. This means that the object's velocity changes over time, instead of maintaining a constant speed or direction.

## 4. What are some real-life examples of trapezoidal motion?

Trapezoidal motion can be observed in many real-life scenarios, such as a car accelerating and decelerating on a highway, a rollercoaster going up and down hills, or a person swinging on a swing set. It can also be seen in industrial machinery, such as robots and cranes, as they move materials in a controlled and efficient manner.

## 5. How is trapezoidal motion useful in engineering and physics?

Trapezoidal motion is useful in engineering and physics because it allows for precise control and manipulation of an object's motion. By carefully calculating the acceleration and deceleration times, engineers can design machines and structures that move smoothly and efficiently. In physics, trapezoidal motion is also used to analyze the movement of objects and predict their trajectories, making it a valuable tool for understanding the physical world.