Leg Configurator Double 4 Bar double grounded inverted

Expression 18: "r" Subscript, "L" 3 , Baseline equals 0.0 7 1 6

0.0 1

0.1

Expression 19: "r" Subscript, "L" 4 , Baseline equals "r" Subscript, "L" 3 , Baseline

equals

0.0 7 1 6

Servo and Ground Position Definition

Calculating Servo Arm Position

Function Definitions

Calculating Knee Joint Location

First we calculate the relative angle of a line between the ground point and the end of the servo arm

Expression 52: theta Subscript, "g" "s" "a" 1 , Baseline equals "a" left parenthesis, "x" Subscript, "s" "a" 1 , Baseline , "y" Subscript, "s" "a" 1 , Baseline , "x" Subscript, "g" , Baseline , "y" Subscript, "g" , Baseline , right parenthesis

equals

negative 1.3 5 9 3 2 6 6 1 8 6 8

Now we solve for the location of the joint between links 1 and 2. First we calculate the angle between the ground connector and the end of the servo arm.

Expression 54: theta Subscript, 1 , Baseline equals "c" left parenthesis, "d" left parenthesis, "x" Subscript, "s" "a" 1 , Baseline , "y" Subscript, "s" "a" 1 , Baseline , "x" Subscript, "g" , Baseline , "y" Subscript, "g" , Baseline , right parenthesis , "r" Subscript, "L" 1 , Baseline , "r" Subscript, "L" 2 , Baseline , right parenthesis

equals

1.0 0 5 2 0 2 7 9 4 0 1

Now we solve for the location of the "knee" joint.

Étiquette masqué left parenthesis, "x" Subscript, "k" , Baseline , "y" Subscript, "k" , Baseline , right parenthesis

Étiquette

equals

left parenthesis, negative 0.0 1 9 6 6 5 3 , 0.0 7 3 7 7 5 5 5 , right parenthesis

Note: There are two solutions to this problem. Which one we get depends on whether we add or subtract the angles in the following steps. Some logic is needed to distinguish which solution to use in certain situations.

Expression 58: "x" Subscript, "k" , Baseline equals "x" Subscript, "g" , Baseline plus "r" Subscript, "L" 1 , Baseline cosine left parenthesis, theta Subscript, "g" "s" "a" 1 , Baseline minus theta Subscript, 1 , Baseline , right parenthesis

equals

negative 0.0 1 9 6 6 5 2 9 6 1 0 2 8

Expression 59: "y" Subscript, "k" , Baseline equals "y" Subscript, "g" , Baseline plus "r" Subscript, "L" 1 , Baseline sine left parenthesis, theta Subscript, "g" "s" "a" 1 , Baseline minus theta Subscript, 1 , Baseline , right parenthesis

equals

0.0 7 3 7 7 5 5 4 6 0 7 3 4

Expression 60: left parenthesis, left parenthesis, 1 minus "t" , right parenthesis "x" Subscript, "s" "a" 1 , Baseline plus "t" "x" Subscript, "k" , Baseline , left parenthesis, 1 minus "t" , right parenthesis "y" Subscript, "s" "a" 1 , Baseline plus "t" "y" Subscript, "k" , Baseline , right parenthesis

Minimum du domaine t:

less than or equal to "t" less than or equal to

Maximum du domaine t:

Expression 61: left parenthesis, left parenthesis, 1 minus "t" , right parenthesis "x" Subscript, "g" , Baseline plus "t" "x" Subscript, "k" , Baseline , left parenthesis, 1 minus "t" , right parenthesis "y" Subscript, "g" , Baseline plus "t" "y" Subscript, "k" , Baseline , right parenthesis

Minimum du domaine t:

less than or equal to "t" less than or equal to

Maximum du domaine t: 1

Calculating Second Knee Joint Location

Calculating Ankle Joint Location

propulsé par