who was it that had a problem about robotic arms a while back

heres something that might help, i found it while cleaning out a backpack from a couple of semesters ago

"Consider the double-jointed robotic arm shown. Let the lower arm be modeled by a = {4, 1, 4}, middle arm be modeled by b = {5, 5, -4}, and upper arm modeled by c = {4, -1, -3}, units are in feet. [A] Find vector "d" for which represents the position of the hand. [B] Find distance of hand from origin.

[A] - its pretty much a summation problem, where d = a + b + c, so plug in {4,1,4} + {5,5,-4} + {4,-1,-3}, and you find that d = {13,5,-3}

[B] - ok, so "distance from origin" is a fancy way of saying "magnitude", or lldll. to find magnitude, you take a, b and c from {13,5,-3} respectively, and plug them into a magnitude equation: lldll = root(a^2+b^2+c^2)

so pretty much, square a,b and c, add them together, and then find their square root. after the math, you get that root(169+25+9) = root(203) = 14.25, so the hand will be 14.25 feet away from the origin



i hope it helps

who do you think op


and no this doesnt help because the problem of inverse kinematics is, given a matrix of 3d coordinates in a motion of the arm, you have to solve for all of the possible (and then throw out impossible solutions and pick the "best" one) angles for each joint in the robot

so if i have coordinate (13,5,8), the arm or leg needs to determine its location in 3d space and then determine at what angle to rotate each arm to reach the end position, then, if there is an answer (because the coordinate could be longer than the combined length Σ||n_i|| which can be determined using your math problem), determine which is correct (assuming there isn't only one solution) and make those movements

you have a single vector but you cant split it into component vectors unless the arm has one joint

"because the coordinate could be longer than the combined length Σ||ni|| which can be determined using your math problem"

assuming youre using these exact coordinates

if you displace the hand, for example, as vector d, you get a new {x,y,z}

so, you need to find the angle of reference (from 0 degrees), where you would use the equations [cos A = (A/llvll), cos B = (B/llvll) and cos C = (C/llvll)]

llvll can be found if you have an equation for v (which is v = ai + bj + ck)

youll want to use cosine for the angle, because for these vector problems, we say that the y-axis is our "imaginary axis" (don't ask why lol, takes too long to explain) in simple trigonometry up to vector analysis

if it means anything, v = llvll [cosAi + cosBj + cos Ck]

salty wrote:you have a single vector but you cant split it into component vectors unless the arm has one joint

for a "multi-jointed" arm, we assume that each joint would be thought of like an origin (THOUGH OF, doesn't necessarily mean it is an origin), because if displace the lower arm, you can displace the other arms because on which reference angle you want to play with

i have no knowledge in robotics, this is from what i can say from an applied math problem from long ago

if you want to find angles based on displacement (going from {x1, y1, z1} to {x2, y2, z2}), use these equations

[cos aplha = (A/llvll), cos beta = (B/llvll) and cos gamma = (C/llvll)] for angles for each respective vector

(llvll can be found if you have an equation for v which is v = ai + bj + ck)

v = llvll [cos(alpha)i + cos(beta)j + cos(gamma)k] for the entire vector
.

will consider this (also i know how to do trig and what vectors are you jew im not a freshman in high school)

ideally there are at least three joints per leg so this isnt a very fun problem to solve im gonna work on it later because i have a project with avr's i wanna work on over thanksgiving break

salty wrote:will consider this (also i know how to do trig and what vectors are you jew im not a freshman in high school)

ideally there are at least three joints per leg so this isnt a very fun problem to solve im gonna work on it later because i have a project with avr's i wanna work on over thanksgiving break

three joints per leg? what does the leg even look like lol, is it like the one i drew?

id assume that in robotics (im not a robotics expert), youd want to find each angle of reference for each joint (acting as if the joint was at a fixed 180 angle, like the x-axis), right?

yes each servo only rotates on one axis and is confined to each one (3 dof; one to rotate on the x axis, one on the y axis, and one on the z axis)

i drew another explanatory diagram will upload tomorrow

ok, but link it to imgur, OTx pictures don't show up for me for some odd reason

and also please draw a xyz graph on each joint to know where your angle of reference has to be