Chain drive 1C
Chain coupling
Coil spring coupling 1
Due to revolution joints of the spring supports (in pink) this coupling can
compensate a large offset of the shaft axes.
For this simulation:
Coupling outer dia. = 20 mm
Offset = 1 mm
Velocity variation is considerable.
Coil spring coupling 2
Due to spherical joints of the spring supports (in pink) this coupling can
compensate a large offset of the shaft axes and a large angular
misalignment between them.
For this simulation:
Coupling outer dia. = 20 mm
Offset = 1 mm
Angular misalignment = 4 deg.
Velocity variation is considerable.
Oldham coupling 1
Oldham coupling 2
An embodiment of Oldham coupling
Axial dimenssion is reduced in comparison with “Oldham coupling 1”.
Oldham coupling 3
An embodiment of Oldham coupling.
Axial dimenssion is reduced. Cylindrical joints are used instead of
prismatic ones. It looks like Cardano coupling but it is totally diferent.
Parallel link coupling
The absence of backlash makes this parallel coupling a precision, lowcost
replacement for gear or chain drives that can also rotate parallel
shafts. Any number of shafts greater than two can be driven from any
one of the shafts, provided two conditions are fulfilled:
1. All cranks must have the same length.
2. The two polygons formed by shafts centers on the moving and
grounded frames must be identical.
The main disadvantage of this mechanism is its dynamic unbalance. The
moving frame should be made as light as possible. The mechanism can not be used for
high speed.
Application of parallelogram mechanism 1
Transmission of rotation movement between parallel shafts.
Application of parallelogram mechanism 2
Transmission of rotation movement between parallel shafts
Application of parallelogram mechanism 3
Transmission of rotation movement between parallel shafts
The red disk rotates without fixed bearing.
Schmidt coupling
Transmission of rotation movement between parallel shafts.
The pink link rotates without fixed bearing.
Both shafts can move during transmission.
Pin coupling 1
The pins are arranged on circles of equal radius on the two shafts
A = R1 + R2
A: Axis distance of the two shafts (eccentricity)
R1: Rose pin's radius
R2: Green pin's radius
Thus the coupling meets conditions of a parallelogram mechanism.
It is a constant velocity coupling.
Numbers of pins on the two shafts must be equal.
Pin coupling 2
The pins and the holes are arranged on circles of equal radius on the two
shafts
A = R2 - R1
A: Axis distance of the two shafts (eccentricity)
R2: Rose hole's radius
R1: Green pin's radius
Thus the coupling meets conditions of a parallelogram mechanism.
It is a constant velocity coupling.
This type of mechanism can be installed in epicyclic reduction gear boxes. See:
Pin coupling 3
An embodiment of Pin Coupling 1
when R1 is different from R2 and pin’s radius is larger than
shaft’s radius. Transmission ratio is 1.
The mechanism now looks like a gear drive but the two shafts
rotate the same direction.
It has a high sensitivity to error in distance between the shaft
axes.
Pin coupling 4
An embodiment of Pin Coupling 1
when R1 is different from R2, number of pins on each disks is 22. Pins
on the pink disk is of lens shape because their radius is too large.
Transmission ratio is 1.
Pin coupling 5
An embodiment of Pin Coupling 3
when:
- R1 is different from R2
- pins radius are larger than shafts radius
- number of pins is infinite so screw surfaces are created.
The working surface of the blue shaft is created when a circle of radius 10 (in the plane
perpendicular to the shaft axis, its center is 5 from the shaft axis) moves along a helix of
pitch 20. The working surface of the pink shaft is created similarly by a circle of radius 15 (in
the plane perpendicular to the shaft axis, its center is 5 from the shaft axis) moving along a
helix of pitch 20. Distance between the shafts is 25.
Transmission ratio is 1. The mechanism now looks like a gear drive but the two shafts
rotate the same direction.
Pin coupling 7
An embodiment of Pin Coupling1.
when number of pins is infinite so screw surfaces are created.
The working surface of each shaft is created when a circle of radius 5
(in the plane perpendicular to the shaft axis, its center is 20 from the
shaft axis) moves along a helix of pitch 40. Distance between the shafts
is 10.
Transmission ratio is 1. The two shafts rotate the same direction.
The mechanism is pourely imaginary product, perhaps no practise application.
Pin coupling 8
An embodiment of Pin Coupling7
when the number of working surfaces is 3.
Transmission ratio is 1. The two shafts rotate the same direction.
The mechanism is pourely imaginary product, perhaps no practise
application.
Universal joint 1
Axles of the two shafts may be
1. Parallel and coincident
2. Parallel and distinct (with eccentricity)
3. Intersecting
4. Skew
It is a constant velocity joint for cases 1, 2 and 3.
For details see:
http://meslab.org/mes/threads/20223-Khop-truc-ngam
Universal joint 2
This low torque joint allows axial shaft movement.
The angle between shafts must be small.
Output velocity is not constant.
Universal joint 3
This pump type coupling has the reciprocating action of
sliding rods in cylinders.
Centers of spherical joints are always in the plane that
bisects the angle α between the two shafts even when α
changes so it is a constant velocity joint.
Pin universal joint
It is a constant velocity joint.
There is a spherical joint between pink shaft and green one.
For each shaft the opposite contact straight lines must be symmetric
about the rotary axis and have a common intersection point with it.
Angle between the two shafts reaches up to 30 deg. in this video.
The mechanism can not be used for reversing rotation because of
large backlash.
Study of Cardan universal joint 1
Universal joints allow to adjust A angle between input and output
shafts even during rotary transmission. This case shows +/- 45
deg regulation. It is clear that single Cardan joint is not of
constant velocity when A differs from 0 deg.
Study of double cardan universal joint 1a
Double Cardan drives allow to adjust relative linear positions
between the input and output shafts even during rotary
transmission. The output velocity is always equal to the input one
(constant velocity joint) because their shafts are kept parallel each
other.
The pin axles on the intermediate half shafts (in yellow and in violet) must be parallel each
other.
Tracta joint 1
It is a constant velocity joint.
There are a revolution joints between:
- orange male swivel and yellow female swivel.
- orange male swivel and green shaft
- yellow female swivel and pink shaft
Axes of cylindrical surfaces on each swivel are skew to each
other at an angle of 90 deg.
The video shows the transmission when angle between two
shafts is 0 deg. and then 30 deg.
Tracta joint 2
It is a constant velocity joint, an embodiment of mechanism shown
in “Tracta joint 1”.
Yellow swivel and orange one are identical.
There are a revolution joints between:
- orange swivel and pink disk.
- yellow swivel and pink disk.
- orange swivel and green shaft
- yellow swivel and blue shaft
Axes of cylindrical surfaces on each swivel are skew to each other at an angle of 90 deg.
The video shows the transmission when angle between two shafts is 0 deg. and then 25
deg.
Rzeppa joint 1
Red bar and yellow shaft create a joint of class II (allowing four
degrees of freedom).
Red bar and green shaft create a joint of class II.
Red bar and blue retainer create a spherical joint.
With this arrangement, the plane containing ball centers almost
always remains in a plane that bisects the angle α between the
two shafts when α changes. See: “Slider crank and coulisse mechanism 1”
The video shows the transmission when α is 0 deg. and then 30 deg.
The output shaft rotates nearly regularly with max error of 1.5% at α = 30 deg.
Tripod joint 1
Pink spherical rollers slide in grooves of yellow shaft. Changes in
the drive angle causes the rollers to move backwards and
forwards along the grooved track as the joint rotates through one
revolution. A small clearance is given between the roller and track
to permit this movement.
The video shows the transmission when α (angle between two
shafts) is 0 deg. and then 15 deg.
The simulation shows that the output shaft rotates nearly regularly with max error of 3.4% at
α = 15 deg.
Birfield joint 1
There is an offset between center of circular grooves on each
shaft and the clutch center (see upper picture). Balls are
positioned by the contact with the grooves.
With this arrangement, the plane containing ball centers always
remains in a plane that bisects the angle α between the two
shafts when α changes to meet condition of constant velocity.
Weiss joint 1
There is an offset between center of circular grooves on each
shaft and the clutch center (see upper picture). Each pink ball is
positioned by the contact with grooves on both shafts and blue
central ball. The latter can rotate around red pin.
With this arrangement, the plane containing ball centers always
remains in a plane that bisects the angle α between the two
shafts when α changes to meet condition of constant velocity.
Spherical 4R mechanism 1b
Spherical: Joint center lines intersect at a common point.
Angle between center lines of revolute joints:
for the orange input link is γ = 20 deg.
for the green output link is β = 90 deg.
for the blue link is α = 90 deg.
for the base link is δ = 15 deg.
The output link revolves irregularly.
Its 1 rev. corresponds 1 rev. of the orange input link.
Angular Transmission 4R Mechanism 2
Two spherical 4R mechanisms are connected back to
back.
4R: 4 revolute joints.
In each mechanism the center lines of 4 revolute joints intersect at a common point.
The angle between center lines of revolute joints for the orange link is not 90 deg. (rather
than Cardan joints).
Angle between the input and output is A = 90 deg.
Angle between cylinder of the orange link and the input shaft is B = A/2 = 45 deg.
This condition makes the mechanism a constant-velocity joint.
The orange link rotates without fixed bearing.
Angular Transmission 4R Mechanism 1
This is the double Cardan.
Angle between the input and output is A = 90 deg.
The orange S-link has a virtual axle.
Angle between the virtual axle of the orange S-link and the input shaft is B = A/2 = 45 deg.
This condition makes the mechanism a constant-velocity joint.
The orange link rotates without fixed bearing.
Spherical 4R mechanism 2a
Axles of revolution joints must be concurrent.
Input: Green shaft, constant speed.
Output: Blue shaft, variable speed.
Spherical 4R mechanism 2b
Combination of two “Spherical 4R mechanism 2a”.
It is a constant velocity joint.
Spherical 4R mechanism 2c
Modification of “Spherical 4R mechanism 2a” and “Spherical 4R
mechanism 2b”.
It is a constant velocity joint.
Spherical 4R mechanism 2d
Persian joint.
It is a modification of “Spherical 4R mechanism 2c” by adding
more connecting rods for balancing.
It is a constant velocity joint.
Spherical 4R mechanism 2e
Modification of “Spherical 4R mechanism 2a” and “Spherical 4R
mechanism 2b”.
It is a constant velocity joint.
Spherical 4R mechanism 2f
Persian joint.
It is a modification of “Spherical 4R mechanism 2e” by adding more
connecting rods for balancing.
Acute angle between input and output shafts is 60 deg.
It is a constant velocity joint.
Spherical 4R mechanism 2g
Persian joint.
It is a modification of “Spherical 4R mechanism 2e” by adding more
connecting rods for balancing.
Angle between input and output shafts is 90 deg.
It is a constant velocity joint.
Bevel Gear Coupling 1
Rotation directions of the drive and driven shafts are opposite.
Angle between them can be ±75 degrees.
Bevel Gear Coupling 2
Combination of two bevel gear couplings.
Relative position of two shafts can be arbitrary, even skew.