Mechanisms

Summary

Mechanisms
Functions
Parallel_3RPR	Constructs the Manipulator object of a planar 3-R P R manipulator.
Parallel_3RPR_full	Constructs the Manipulator object of a planar 3-R P R manipulator.
Parallel_3PRR	Constructs the Manipulator object of a 3- P R R manipulator.
ParallelPRP2PRR
Parallel_RPRRP	Constructs the Manipulator object of a R P R R P manipulator.
Parallel_RR_RRR	Constructs the Manipulator object of a 2-R R manipulator.
Parallel_PRRP	Constructs the Manipulator object of a P R R P manipulator.
Orthoglide	Constructs the Manipulator object of the Orthoglide manipulator.
ParallelRPR2PRR	Constructs the Manipulator object of the R P R 2-P R R manipulator.
Parallel3PPPS	Constructs the Manipulator object of the 3- P P P S manipulator.
Serial3R	Constructs the Manipulator object of the serial 3R manipulator.
Parallel3PRSd	Constructs the Manipulator object of the 3- P R S manipulator.
Parallel3PRSc	Constructs the Manipulator object of the 3- P R S manipulator.

Functions

Parallel_3RPR

Parallel_3RPR := proc( {
d1 ::algebraic := 17.04,
d2 ::algebraic := 16.54,
d3 ::algebraic := 20.84,
beta ::algebraic := arccos ((d2^2-d3^2-d1^2)/(-2*d3*d1)),
A2x ::algebraic := 15.91,
A3x ::algebraic := 0,
A3y ::algebraic := 10,
precision ::integer := 4
}
,
morespec ::seq(name=algebraic),
moreranges ::seq(name=range)    )

Constructs the Manipulator object of a planar 3-R P R manipulator.

Parameters

name = constant

the geometric parameters of the robot (see Figure1),

Figure1

where name is one of d1, d2, d3, beta, A2x, A3x, A3y,
and constant is a numerical value.
All the variables d1, d3, A2x, A3x, A3y must be assigned.
One of d2, beta must be assigned (if both are assigned, d3 is ignored).
By default, the values are d1 = 17.04, d2 = 16.54, d3 = 20.84, A2x = 15.91, A3x = 0, A3y = 10.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar 3-R P R manipulator whose dimensions are given in input.

Example

> robot := Parallel_3RPR (d1=3, d2=4, d3=5, A2x=5, A3x=0, A3y=5):
> robot[Equations];
         2           2         2      2          2
[cosAlpha  + sinAlpha  - 1, B1x  + B1y  - R1, B1x  + 6 B1x cosAlpha - 10 B1x

                 2                         2                              2
     + 9 cosAlpha  - 30 cosAlpha + 25 + B1y  + 6 B1y sinAlpha + 9 sinAlpha

              2                                                2
     - R2, B1x  + 6 B1x cosAlpha - 8 B1x sinAlpha + 25 cosAlpha

                  2      2
     + 25 sinAlpha  + B1y  + 8 B1y cosAlpha + 6 B1y sinAlpha - 10 B1y

     - 40 cosAlpha - 30 sinAlpha + 25 - R3]

Parallel_3RPR_full

Parallel_3RPR_full := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of a planar 3-R P R manipulator.

Parameters

name = constant

the geometric parameters of the robot (see Figure1),

Figure1

where name is one of d1, d2, d3, beta, A2x, A3x, A3y,
and constant is a numerical value.
All the variables d1, d3, A2x, A3x, A3y must be assigned.
One of d2, beta must be assigned (if both are assigned, d3 is ignored).
By default, the values are d1 = 17.04, d2 = 16.54, d3 = 20.84, A2x = 15.91, A3x = 0, A3y = 10.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar 3-R P R manipulator whose dimensions are given in input.

Parallel_3PRR

Parallel_3PRR := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of a 3- P R R manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of l1, l2,
and constant is a numerical value.
By default, the values are l1 = 1, l2 = 1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar P R R P manipulator whose dimensions are given in input.

Example

> robot := Parallel_3PRR (l1=1,l2=1):
> robot[Equations];

TODO

ParallelPRP2PRR

ParallelPRP2PRR := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the *Manipulator* object of a P R P

2 P R R manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of l1, l2, a, b,
and constant is a numerical value.
By default, the values are l1 = 1, l2 = 1.5, a = 1, b = 1.2

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A *Manipulator* data structure representing the planar 2 P R R

P R P manipulator whose dimensions are given in input.

Example

> robot := ParallelPRP2PRR (l1=1,l2=1):
> robot[Equations];
      2                                     2                         2    2
[1 - x  + 2 x cos(phi) + 2 x rho1 - cos(phi)  - 2 cos(phi) rho1 - rho1  - y

                              2       2
     + 2 y sin(phi) - sin(phi) , 1 - x  - 12/5 x cos(phi) + 2 x rho2

       36         2                            2    2
     - -- cos(phi)  + 12/5 cos(phi) rho2 - rho2  - y  - 12/5 y sin(phi)
       25

       36         2
     - -- sin(phi) , -4 x cos(phi) + 4 cos(phi) rho3 - 4 y sin(phi)]
       25

Parallel_RPRRP

Parallel_RPRRP := proc( {
e ::constant := 0.7,
L4 ::constant := 1,
S2min ::constant := 0.5,
S2max ::constant := 1.5,
S4min ::constant := 0.1,
S4max ::constant := 1.1,
precision := 4
}
,
morespec ::seq(name=algebraic)    )

Constructs the Manipulator object of a R P R R P manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of e, L4, S2min, S2max, S4min, S4max,
and constant is a numerical value.
By default, the values are e = 0.7, L4 = 1, S2min = 0.5, S2max = 1.5, S4min = 0.1, S4max = 1.1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar R P R R P manipulator whose dimensions are given in input.

Example

> robot := Parallel_RPRRP (e=1,L4=1):
> robot[Equations];

Parallel_RR_RRR

Parallel_RR_RRR := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of a 2-R R manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of e, l1, l2, l3, l4,
and constant is a numerical value.
By default, the values are e = 1, l1 = 1, l2 = 1, l3 = 1, l4 = 1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar 2-R R manipulator whose dimensions are given in input.

Example

> robot := Parallel_RR_RRR (e=1,L4=1):
> robot[Equations];

Parallel_PRRP

Parallel_PRRP := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of a P R R P manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of l1, l2,
and constant is a numerical value.
By default, the values are l1 = 1, l2 = 1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the planar P R R P manipulator whose dimensions are given in input.

Example

> robot := Parallel_PRRP (l1=1,l2=1):
> robot[Equations];

Orthoglide

Orthoglide := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of the Orthoglide manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of l1, l2,
and constant is a numerical value.
By default, the values are l1 = 1, l2 = 1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the Orthoglide manipulator whose dimensions are given in input.

Example

> robot := Orthoglide (l1=1,l2=1,l3=1):
> robot[Equations];

ParallelRPR2PRR

ParallelRPR2PRR := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of the R P R 2-P R R manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of a, b, L2, L3,
and constant is a numerical value.
By default, the values are a = 1, b = 4, L2 = 2, L3 = 2.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the Orthoglide manipulator whose dimensions are given in input.

Example

> robot := ParallelRPR2PRR ():
> robot[Equations];

Parallel3PPPS

Parallel3PPPS := proc( morespec ::seq(name=algebraic),
precision := 4,
{
quaternions ::truefalse := false,
tiltandtorsion ::truefalse := false,
normalize ::truefalse := false,
ortho ::truefalse := false
}    )

Constructs the Manipulator object of the 3- P P P S manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is either one of Ax, Ay, Az, Bx, By, Bz, Cx, Cy, Cz, or one of L1, L2, L3.
and constant is a numerical value.
By default, the values are Ax = 1, Ay = 0, Az = 0, Bx = 0, By = 1, Bz = 0, Cx = 0, Cy = 0, Cz = 1, and L1 = (Bx-Ax)^2 + (By-Ay)^2 + (Bz-Az)^2, L2 = (Cx-Bx)^2 + (Cy-By)^2 + (Cz-Bz)^2, L3 = (Ax-Cx)^2 + (Ay-Cy)^2 + (Az-Cz)^2.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the Orthoglide manipulator whose dimensions are given in input.

Example

> robot := Parallel3PPPS ():
> robot[Equations];

Serial3R

Serial3R := proc( morespec ::seq(name=algebraic),
precision := 4 )

Constructs the Manipulator object of the serial 3R manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of theta1, d2, d3, d4, r2, r3,
and constant is a numerical value.
By default, the values are theta1 = 0, d2 = 1, d3 = 0.5, d4 = 0.8, r2 = 0.15, r3 = 0.1.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the Orthoglide manipulator whose dimensions are given in input.

Example

> robot := Serial3R ():
> robot[Equations];

Parallel3PRSd

Parallel3PRSd := proc( morespec ::seq(name=algebraic),
precision := 4,
{
quaternions ::truefalse := false,
tiltandtorsion ::truefalse := false,
ortho ::truefalse := false,
normalize ::truefalse := false
}    )

Constructs the Manipulator object of the 3- P R S manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of r, l.
and constant is a numerical value.
By default, the values are r = 1.3 and *l*=1.5.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the 3- _P R S manipulator with parallel prismatics, whose dimensions are given in input.

Example

> robot := Parallel3PRSd ():
> robot[Equations];

Parallel3PRSc

Parallel3PRSc:= proc( morespec ::seq(name=algebraic),
precision := 4,
{
quaternions ::truefalse := false
}    )

Constructs the Manipulator object of the 3- P R S manipulator.

Parameters

name = constant

the geometric parameters of the robot,

where name is one of r, l.
and constant is a numerical value.
By default, the values are r = 1.3 and *l*=1.5.

precision = integer (optional)

the precision, where integer is the number of significative digits; default value: 4.

Returns

A Manipulator data structure representing the Orthoglide manipulator whose dimensions are given in input.

Example

> robot := Parallel3PRSc ():
> robot[Equations];