- #1
MStoffle
- 3
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Hello, I am working on a project where I am trying to find the weight distribution on a 4 wheeled vehicle that is traveling diagonally up an incline. You can effectively think of the vehicle as having a pitch and a yaw angle in the body frame. Using an arbitrary location of the total center of mass, I tried using equilibrium equations to find the reaction forces of all the wheels, but after taking sum of forces and moments to be zero about one of the wheels, the problem appears to be statically indeterminate. I am particularly interested in the normal component reaction forces of the wheel so I can continue a traction model for the vehicle facing any direction on the incline. I have provided imgur links to two pictures of my notes for the scenario (It may appear sloppy and I apologize) for better reference and you can see that with the end equations, I would particularly be interested in the first, second, and fourth equations for the z components, but that is still 3 equations with 4 unknowns.
https://imgur.com/3ON5rOs
https://imgur.com/j3g1zuF
I opened these images and noticed they may be blurry. The equations I have come up with taking moments about the front left wheel:
Fz,FR*(-d) + Fz,RR*(-d) + Wy,cg*(-h) + Wz,cg*(c) = 0
Fz,RL*(-b) + Fz,RR*(-b) + Wx,cg*(h) + Wz,cg*(a) = 0
Fx,FR*(-d) + Fy,RL*(-b) + Fx,RR*(-d) + Fy,RR*(-b) + Wx,cg*(c) + Wy,cg*(a) = 0
Fz,FL + Fz,FR + Fz,RL + Fz,RR - Wz,cg = 0
The other 2 remaining equations would relate sum of forces in the x and y direction.
What can I do from here to solve this problem? Am I missing something?
Any advice is greatly appreciated!
https://imgur.com/3ON5rOs
https://imgur.com/j3g1zuF
I opened these images and noticed they may be blurry. The equations I have come up with taking moments about the front left wheel:
Fz,FR*(-d) + Fz,RR*(-d) + Wy,cg*(-h) + Wz,cg*(c) = 0
Fz,RL*(-b) + Fz,RR*(-b) + Wx,cg*(h) + Wz,cg*(a) = 0
Fx,FR*(-d) + Fy,RL*(-b) + Fx,RR*(-d) + Fy,RR*(-b) + Wx,cg*(c) + Wy,cg*(a) = 0
Fz,FL + Fz,FR + Fz,RL + Fz,RR - Wz,cg = 0
The other 2 remaining equations would relate sum of forces in the x and y direction.
What can I do from here to solve this problem? Am I missing something?
Any advice is greatly appreciated!