1998 summer q2 forward kinematics
DESCRIPTION
1998 Summer Q2 Forward Kinematics. Use the DH Algorithm to assign the frames and kinematic parameters. 4-Tool Pitch. 3. 2. 5-Tool Pitch. 1. Number the joints 1 to n starting with the base and ending with the tool yaw, pitch and roll in that order. - PowerPoint PPT PresentationTRANSCRIPT
1998 Summer Q2 Forward Kinematics
Use the DH Algorithm to assign the frames and kinematic parameters
Number the joints 1 to n starting with the base and ending with the tool yaw, pitch and roll in that order.
The location of frame origins is ascertained only when the staps of the algorithm are carried out.
1
2
34-Tool Pitch
5-Tool Pitch
Note: There is no tool yawno tool yaw in this case
Assign a right-handed orthonormal frame L0 to the robot base, making sure that z0 aligns with the axis of joint. Set K=1
z0 y0
x0
Frame 0
z0 y0
x0
Align zk with the axis of joint k+1.
z1
Locate the origin of Lk at the intersection of the zk and zk-1axes
Frame 1
z0 y0
x0
z1
Select xk to be orthogonal to both zk and zk-1.
Select yk to form a right handed orthonormal co-ordinate frame Lk
y1 will be hidden after this for the purpose of clarity
x1
y1Frame 1
z0 y0
x0
z1x1
Align zk with the axis of joint k+1.
This is the line of action of the prismatic joint
z2
Frame 2
z0 y0
x0
z1x1
z2
Select xk to be orthogonal to both zk and zk-1.
Select yk to complete the right handed orthonormal co-ordinate frame
x2
y2Frame 2
z0 y0
x0
z1x1
z2y2
Align zk with the axis of joint k+1.
Locate the origin of Lk at the intersection of the zk and zk-1axes
z3
x2
Frame 3
z0 y0
x0
z1x1
z2y2
z3
Select xk to be orthogonal to both zk and zk-1.
x3
Select yk to complete the right handed orthonormal co-ordinate frame
y3
x2
Frame 3
z0 y0
x0
z1x1
z2y2
z3
x3
y3
Align zk with the axis of joint k+1, the tool roll joint
The origin is actually at the same point as that of the tool pitch joint
z4
x2
Frame 4
z0 y0
x0
z1x1
z2y2
z3
x3
y3
z4
Select xk to be orthogonal to both zk and zk-1.
x4
Select yk to complete the right handed orthonormal co-ordinate frame
y4
x2
Frame 4
z0 y0
x0
z1x1
z2
y2
z3
x3
y3
z4
x4
y4
Set the origin of Ln at the tool tip. Align zn with the approach vector of the tool.
Align yn with the sliding vector of the tool.
Align xn with the normal vector of the tool.
z5
y5x5
x2
Frame 5
With the frames assigned the kinematic parameters can be determined.
z0 y0
x0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
z0 y0
x0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
Locate point bk (b5) at the intersection of the xk and zk-1 axes. If they do not intersect, use the intersection of xk with a common normal
between xk and zk-1
b5k = 5
z0 y0
x0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2 bk
Compute k as the angle of rotation from xk-1 to xk measured about zk-1
It can be seen here that the angle of rotation from xk-1 to xk about zk-1 is -90 degrees i.e. 5 = -90º
But this is only for the soft home position, 5 is the joint variable.
5
k = 5
z0 y0
x0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2 b5
5
Compute dk as the distance from the origin of frame Lk-1to point bk along zk-1
d5
Remember the roll joint frame is just moved out of position for clarity
Compute ak as the distance from point bk to the origin of frame Lk along xk
In this case these are the same point therefore a5=0
k = 5
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2 b5
5
d5
Compute k as the angle of rotation from zk-1 to zk measured about xk
It can be seen here that the angle of rotation from z4 to z5 about x5 is zero i.e. 5 = 0º
k = 5
Locate point bk at the intersection of the xk and zk-1 axes. If they do not intersect, use the intersection of xk with a common normal
between xk and zk-1
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b4
5
d5
k = 4
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b4
5
d5
Compute k as the angle of rotation from xk-1 to xk measured about zk-1
It can be seen here that the angle of rotation from xk-1 to xk about zk-1 is zero i.e. 4 = 0º
k = 4
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b4
5
d5
As the origin of both frames are at the same point the a and d values are zero in this case, ie a4=0 and d4=0
Compute k as the angle of rotation from zk-1 to zk measured about xk
It can be seen here that the angle of rotation from z3 to z4 about x4 is -90º i.e. 4 = -90º
k = 4
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2bk
5
d5
Locate point bk at the intersection of the xk and zk-1 axes. If they do not intersect, use the intersection of xk with a common normal
between xk and zk-1
k = 3
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2bk
5
d5
Compute k as the angle of rotation from xk-1 to xk measured about zk-1
It can be seen here that the angle of rotation from x2 to x3 about z2 is 180º i.e. 3 = 180º
k = 3
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2b3
5
d5
Compute dk as the distance from the origin of frame Lk-1to point bk along zk-1
This is the joint variable for joint 3 which is the prismatic joint
d3
Compute ak as the distance from point bk to the origin of frame Lk along xk
In this case these are the same point, therefore a3=0
k = 3
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2b3
5
d5d3
Compute k as the angle of rotation from zk-1 to zk measured about xk
It can be seen here that the angle of rotation from z2 to z3 about x3 is 90º i.e. 3 = 90º
k = 3
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b2
5
d5d3
Locate point bk at the intersection of the xk and zk-1 axes. If they do not intersect, use the intersection of xk with a common normal
between xk and zk-1
k = 2
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
bk
5
d5d3
Compute k as the angle of rotation from xk-1 to xk measured about zk-1
It can be seen here that the angle of rotation from xk-1 to xk about zk-1 is 90º i.e. 2 = 90º
k = 2
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b2
5
d5d3
Compute dk as the distance from the origin of frame Lk-1to point bk along zk-1
This is zero in this case, as bk is at the origin of frame Lk-1 therefore d2 =0
Compute ak as the distance from point bk to the origin of frame Lk along xk
a2
k = 2
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b2
5
d5d3
a2
Compute k as the angle of rotation from zk-1 to zk measured about xk
It can be seen here that the angle of rotation from z1 to z2 about x2 is 90º i.e. 2 = 90º
k = 2
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b1
5
d5d3
a2
Locate point bk at the intersection of the xk and zk-1 axes. If they do not intersect, use the intersection of xk with a common normal
between xk and zk-1
x0
k = 1
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b1
5
d5d3
a2
x0
Compute k as the angle of rotation from xk-1 to xk measured about zk-1
It can be seen here that the angle of rotation from xk-1 to xk about zk-1 is zero i.e. 1 = 0º
k = 1
Compute dk as the distance from the origin of frame Lk-1to point bk along zk-1
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
bk
5
d5d3
a2
x0
d1
Compute ak as the distance from point bk to the origin of frame Lk along xk
This is zero in this case, therefore, a1 = 0.
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2
b1
5
d5d3
a2
x0
d1
Compute k as the angle of rotation from zk-1 to zk measured about xk-1
It can be seen here that the angle of rotation from zk-1 to zk about xk-1 is 90º i.e. 1 =90º
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2 5
d5d3
a2
x0
d1
From this drawing a table of D-H parameters can be compiled
z0 y0
z1
x1
z2
y2
z3 x3
y3
z4
x4
y4
z5
y5x5
x2 5
d5d3
a2
x0
d1
Link θ a d α Home q 1 q1 0 d1 = 0.8m 90o 0o 2 q2 a2=0.15m 0 90o 90o 3 180o 0 q3=d3=0.6+l1 90o 0.6+l1 4 q4 0 0 -90o 0o 5 q5 0 d5=0.55m 0o -90o