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## Main Question or Discussion Point

Hi everyone.

I'm trying to build a robotic "arm" to move an object along one axis, the idea is to put a dc motor connected to an H-brigde which is then controlled by a microcontroller, the dc-motor will be attached to the object I intend to move by a cable.

Since the objective of this is to position the object anywhere i want, i need to correctly calculate in the microcontroller the precise amount of time it should turn the motor on and then off. Also, the faster the object moves to the desired place the better so my idea is to turn on the motor until the object reaches "halfway" and then reverse the motor's polarity so it decelerates quickly until it gets there, and then shut it off.

Could you please help me come up with an equation like P(t) = ?, I mean the function that gives the position of the object as a function of the time the motor is on, supposing it is completely still in the beginning.

I can't really come up with this equation, i've seen this equation in another thread but i don't really get it :

Where

V is the terminal voltage applied to the motor

i is the armature current

w the rotational velocity in rad/s

K the motor backemf/torque constant

R the armature winding resistance

but if this is true then w = (V-R*i ) / K , and if R,K,V are constants then this function is positive at i=0 and becomes negative at some point, how can the angular velocity be positive when supplying no current and then start decelerating and eventually reverse speed if i becomes larger? where is my reasoning flawed? Is the "i" a function of something or a constant when motor is accelerating/decelerating?

Please help me, i would appreciate it very much, don't know anyone who knows enough physics to help me with this, and my physics are limited since I'm a software eng. student.

PS: I know that a stepper motor would be better for this, but I intend to keep the project as cheap as possible.

Again, thanks a lot for all help

I'm trying to build a robotic "arm" to move an object along one axis, the idea is to put a dc motor connected to an H-brigde which is then controlled by a microcontroller, the dc-motor will be attached to the object I intend to move by a cable.

Since the objective of this is to position the object anywhere i want, i need to correctly calculate in the microcontroller the precise amount of time it should turn the motor on and then off. Also, the faster the object moves to the desired place the better so my idea is to turn on the motor until the object reaches "halfway" and then reverse the motor's polarity so it decelerates quickly until it gets there, and then shut it off.

Could you please help me come up with an equation like P(t) = ?, I mean the function that gives the position of the object as a function of the time the motor is on, supposing it is completely still in the beginning.

I can't really come up with this equation, i've seen this equation in another thread but i don't really get it :

**V= R*i + K*w**Where

V is the terminal voltage applied to the motor

i is the armature current

w the rotational velocity in rad/s

K the motor backemf/torque constant

R the armature winding resistance

but if this is true then w = (V-R*i ) / K , and if R,K,V are constants then this function is positive at i=0 and becomes negative at some point, how can the angular velocity be positive when supplying no current and then start decelerating and eventually reverse speed if i becomes larger? where is my reasoning flawed? Is the "i" a function of something or a constant when motor is accelerating/decelerating?

Please help me, i would appreciate it very much, don't know anyone who knows enough physics to help me with this, and my physics are limited since I'm a software eng. student.

PS: I know that a stepper motor would be better for this, but I intend to keep the project as cheap as possible.

Again, thanks a lot for all help