I got problems. And naturally, a lot.

Jan 23rd:

So… How can I find out a suitable gearing in time?

Harmonic gearings are expensive. Because I know nothing about mechanical engineering, though I wish I could have known. I cannot figure out what models or types are proper.
What I know is that there will be a version with cycloidal reducers. And now I can only see the prototype of that. Then my mind goes blank.
Maybe as always I may start with algorithms and controls. These is the only thing I can do now. Come on..
That’s killing me.

Jan 29th:
Forget about the actul solution, just get into theoretical part first.

| Coordinates

1. Joint coordinates

P(angle A1, angle A2, … , angle A6)
A series of figures describing the location of corresponding joints.

2. Tool coordinates

Include data of the tool, such as:
where is the TCP(tool center point)
the geometry of the tool (the orientation of the tool)

The zero point of the coordinate systems is located at the Tool-Center-Point (TCP) of the effector. Usually the coordinates are stated Cartesian, whereas one of the axes have to point into the extended direction of the gripper.

3. World coordinates

Describing the location of the points within the workspace. Here, a work point is specified in the form of coordinates: P(x, y, z)

Feb 4th:
To be honest, I really don’t think I got much from the Theoretical mechanics.
It was just literally a set of practice problems with no one explaining specificlly why and how. Totally disastrous. Hope this helps.

1. DH parameters

They’re four parameters associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain, or robot manipulator.
To tandardize the coordinate frames for spatial linkages.
coordinate frames are attached to the joints between two links such that one transformation is associated with the joint, [Z], and the second is associated with the link [X]. The coordinate transformations along a serial robot consisting of n links form the kinematics equations of the robot,[T]=[Z1][X1][Z2][X2]…[Zn][Xn]
where [T] is the transformation locating the end-link.

In a short time I would definitely need to review this page for many times.

In summary, the reference frames are liad out as follows:

  1. The z-axis is in the direction of the joint axis.
  2. The x-axis is parallel to the common normal: $x_n = z_n \times z_{n-1}$ (or away from)
    If there is no unique common normals (parallel z axes), then d (blow) is a free parameter. Then direction of $x_n$ is from $z_{n-1}$ to $z_n$.
  3. The y-axis follows from the x- and z-axis by choosing it to be a right-handed coordinate system.
    The following four transformation parameters are known as D-H parameters:
    • d: Offset along previous z to the common normal.
    • ϴ: angle about previous z, from old x to new x
    • r: length of the common normal (aka a, but if using this noataion, do not confuse with alpha). Assuming a revolute joint, this is the radius abou previous z.
    • alpha: angle about common normal, from old z axis to new z axis.

| Kinematics

2. Forward and inverse kinematics

Concepts are simple but the algo requires further understanding.

Forward kinematics is the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters
While the inverse one, is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain.

3. Piper Principle

As the inverse kinematic of a robot with high DOF is extremely complex, resulting multiple solutions at the same time, and is usually without closed solution. While if some conditions are met, it is still possible to solve it.

If meets any of the following conditions:

  • Three adjacent joints are cross to one point
  • Three adjacent joints are parallel to each other

Feb 24th:
Current progress and reading speed is limited. Maybe I should have use the Chinese books now. It surely benefits but also takes time.