GB2412360A

GB2412360A - Robotic thumb construction

Info

Publication number: GB2412360A
Application number: GB0406352A
Authority: GB
Inventors: Richard Martin Greenhill; Richard Walker; Matthew Godden; Hugo Elias
Original assignee: Shadow Robot Co Ltd
Current assignee: Shadow Robot Co Ltd
Priority date: 2004-03-22
Filing date: 2004-03-22
Publication date: 2005-09-28
Anticipated expiration: 2024-03-22
Also published as: GB0406352D0; GB2412360B

Abstract

A robotic thumb T has a base portion 6 with two degrees of freedom with a first joint part 13a angled relative to a palm portion F and second joint portion 13b orthogonal to this, second 9 and third 11 phalange portions, each having a joint 21, 23 with the joint 21 being universal and the joint 23 having a single degree of freedom.

Description

241 2360 Artificial hands This invention relates to artificial hands and,

is particuliarly concerned with a construct for an artificial thumb to form part of such hands.

Applicant's co-pending UK Patent Application GB No. 0206974.8 discloses am artificial hand/forearm construction.

Of crucial importance in such a construct is the form of the thumb portion of the hand. The present invention is directed to an artificial thumb which offers the potential for enhanced performance! over that disclosed in the aforesaid PatenApplicationor, indee, over prior art thumb arrangements of which Applicant is aware.

The human thumb incorporates joints nominally of the ball and socket and saddle types, nominal in that the joints, whilst being designated ball and socket or saddle, as the case may be, are constrained for movement only nominally in the manner of such joints.

If an artificial thumb is designed using joints approximating to those found in the human hand, it is difficult to mount sensors at the joints, and without full and accurate sensing of movements at the joints movements of the artificial thumb are difficult to control.

Movements capable of being provided at the joints of a human thumb can with a substantial faithfulness be Reconstructed and emulated by a series of simple one-degree- of-freedom joint elements.

According to the invention, an artificial hand has, inter alla, (a) a frame portion defining a base Cartesian coordinate reference frame; and (b) an artificial thumb, being a thumb which comprises: (i) a metacarpal phalange part; (ii) a medial phalange part; (iii) a distal phalange part; (iv) a two-degree-of-rotational freedom joint coupling said metacarpal phalange part at one end thereof to said frame portion with one of the rotational axes of the rotary part of said joint offset angularly with reference to said base coordinate reference frame; (v) coupling said metacarpal phalange part at the other end thereof to one end of said medial phalange part, a universal joint; and, (vi) coupling said medial phalange part, at the other end thereof, to said distal phalange part at one end thereof, a single-degree-of- rotational freedom joint.

In the arrangement of Fig.3, the two-degree-of-rotational freedom joint 7 comprises two single-degree-of-rotational freedom portions 7a, 7b, respectively, the portion 7a having its rotational axis Z offset angularly with reference to the base coordinate reference frame R. and the other portion 7b having its rotational axis Z orthogonal to the rotational axis Z of said first portion 7a.

The foregoing and other characteristics of a hand as herinbefore described are hereinafter described with reference to the accompanying drawings in which: Fig.1 is a diagram showing, schematically, a thumb in accordance with the invention.

Referring to Fig.1, the artificial hand has, inter alla, (a) a frame portion F defining a base Cartesian coordinate reference frame R; and (b) an artificial thumb T. being a thumb which comprises: (i) a metacarpal phalange part 6; (ii) a medial phalange part 9; (iii) a distal phalange part 11; (iv) a two-degree-of-rotational freedom joint 13 coupling said metacarpal phalange part 6 at one end 15 thereof to said frame portion with one Z of the rotational axes of said joint 13 offset angularly with reference to the base coordinate reference frame R; (v) coupling the metacarpal phalange part 13 at the other end 17 thereof to one end 19 of the medial phalange part 9, a universal joint 21; and, (vi) coupling said medial phalange part 9, at the other end 23 thereof, to said distal phalange part 11 at one end 25 thereof, a single-degree-of- rotational freedom joint 27.

As shown, the two-degree-of-rotational freedom, joint 13 comprises, more particularly, two single-degree-of-rotational freedom portions 13a, lab, respectively, the portion 13a having its rotational axis Z offset angularly with reference to the base coordinate reference frame R. and the other portion 13b having its rotational axis Z orthogonal to the rotational axis Z of said first portion 13a. i

GEOMETRIC MODEL OF A THUMB BY WAY OF

THE DENAVIT-HARTENBERG (D-H)

CONVENTION

1. Basic principles As stated by Lopez and Foulc [1], an articulated mechanical system (AMS) is characterized by two parameters: structural parameters (constant) and articular variables (angles or lengths). Each link in the AMS has assigned a Cartesian coordinate system that can be expressed as a series of transformations from the main reference frame. According to the formalism of Eulerian angles, the relation between one reference frame and the next can be stated as three translations and three rotations, which correspond to the Eulerian angles (at, O. up).

The Denavit-Hartenberg [2] convention' allows us to express a reference frame relative to the previous one by four parameters. These in turn represent the 4 specific transformations the reference frame must undergo in the order dictated. (First Z then X, the rotation and translation order within these is irrelevant). The parameters are: => rotation in Z. r => translation in Z. a => translation in X, a => rotation in X. Transformation = (Rot. in Z by B) x (Trans. m Z by r) x (Trans. in X by a) x (Rot. in X by c) In matrix form we have: T= cost) ffin()Cos(a) sin(O) sin(a) acos() sin(O) cost) cos(a) -cos(O) sin(a) a sin() O sin(a) cos(a) r O O 0 1 1. Many people are not aware that there are two different fonms of D-H representation for sepal-link manipulator kinematics: a.- Classical as per the original 1955 paper of Denavit and Hartenberg and used in textbooks such as by Paul Fu et al or Spong and Vdyasagar. (This is the form being used for this description).

b.- Modified form as introduced by Craig in his text book. [3] -s Filling in each set of 4 parameters (each row in the parameter table) into the previous definition gives a transformation matrix that relates two adjacent frames of reference. Repeating this procedure for the entire set, one gets a number of matrices equal to the degrees of freedom (DOE) of the AMS, and multiplying all these matrices in the appropriate order yields the position and orientation of the end-effector. (See section 3).

Identifying all the quartets of parameters uniquely defines the mechanics of the AMS. It is important to keep in mind however, that there are several different ways, using the D-H convention, to define the same AMS, and they are all equivalent with respect to the mechanics of the AMS. Tables within the same set presented bellow are interchangeable. By interchangeable it is meant that one can achieve the same range of movement and the same orientation space for the tip of the thumb (or endeffector) by simply redefining some of the angles and adjusting me ranges in the mathematical model.

Two sets of tables are now presented. The difference between them is the orientation space achieved by the tip of the thumb (or end-effector). The preferred configuration is that of Set 1, (for which a drawing is included). The other is a slight variant. Set 2 simply has a rotation of 90 along the metacarpal joint in comparison with the preferred configuration of Set 1.

The tables also include a row of off-set parameters that defines the position of the thumb with respect to the palm of the hand. This is not a joint.

For all tables, three of the parameters are constant (r, a, a), and the controlled variable along which the joint moves is (a). The constant parameters (r, a, a) can be set at different values to improve the overall behaviour. For a the range of these values go from [-135, -45] and [45, 135]. For the off-set values the range is the same as for a, except when the value in any of the given tables is +45, in this case the range is [-90,90].

The preferred values are the ones stated in the tables.

2. Denavit-Hartenberg parameters for the thumb Set I Joint number. _ r a a Off-set 0 0 0 -45 1 0 0 0 90 90 d6 0 o 3 0 0 0 90 00 d9 Do 0 dl 1 0 o Joint number a Off-set 0 1 oO O O 90 90 d6 90 o 3 0 0 0 -90 4 0 0 d9 90 o o o O o Set 2 Joint number a Off-set 0 -45 o 1 90 O O 90 90 d6 -90 o 3 00 0 0 90 00 d9 oo 00 dll oo Joint number 0 r a ac Off-set 0 -45 o 90 O O 90 90 d6 0 o 3 00 0 0 -90 0 d9 90 o 0 dl I 0 o

3. Example.

Now follows a brief example of how to use any one of the tables and the transformation matrix given before to understand and reconstruct the thumb and its mechanics. The example will proceed using the first table of Set I. T = cos(0) -sin(0) cos(a) sin(0) sin(a) . a cos(0) sin(0) cos(0) cos(a) cos(0) sin(a) a sin(0) 0 sin(a) cos(a) r O O 0 1 First table of Set I. Joint number a Off-set 0 -45 o 1 0 0 0 90 2 90 0 d6 0 o 0 90 4 0O 0 d9 oo 0 dl 1 0 o We take the first row (Off-set) and substitute the values into the T matrix.

Joint number Off-set 0 -45 o T = cos(0 ) -sin(0 ) cos(-45 ) sin(0 ) sin(-45 ) 0 cos(0 ) sin(0 ) cos(0 ) cos(-45 ) -cos(0 ) sin(45 ) 0 sin(0 ) 0 sin(-45 ) cos(-45 ) 0 O O 0 1 Yielding: Toxt= I O O O 0 0.7071 0.7071 0 0 -0.7071 0.7071 0 O O 0 1 We now do the same for the next row (joint 1). It is important to clarify that since this is a joint (unlike the off-set) , one of the parameters is variable, (O in this case). So the matrix looks like: Joint number | R 1 o 900 To = cos(O) -sin(O) cos(90 ) sin(O) sin(90 ) O cos(O) sin(O) cos(O) cos(90 ) -cos(O) sin(90 ) O sin(O) O sin(90) cos(90 ) O O O 0 1 T'= cos(O) O sin() O sin(O) O -cos(O) O 0 1 0 0 O O 0 1 The O value given in the table for joint 1 (0 = 0 ) refers to the starting position, but may vary. Every time that it changes the value has to be updated and the matrix re-evaluated. We will now use the starting value 0 = 0 .

T'= cos(O ) O sin(O ) O sin(O ) O -cos(0 ) O 0 1 0 0 O O 0 1 T.= | I O O O O O -1 0 0 1 0 0 O O 0 1 Since any joint will always rotate along 0, it means that it will always be rotating around the Z-axis of the coordinate system assigned to the joint in question. This allows us to understand how one joint is rotating with respect to the previous one. It is simply a matter of defining a coordinate system, transforming it according to the parameters in the table and identifying where the new Z- axis is. If one sees the diagram it is easier to understand and notice how the rotation of each joint always matches the Z-axis. 9-

If we now continue going down Table I and substituting the values as we did for joint I, we get the rest of the transformation matrices, (T2, T3, T4, T5). Just for practical purposes of this exercise, the values for d6, d9, dl 1, will be randomly assigned to: d6= 35 units, d9= 30 units, dl 1= 20 units.

T2= O -1 0 0 1 0 0. 35 O 0 1 0 O O 0 1 T3= 1 0 0 0 O O -1 0 0 1 0 0 O O 0 1 T4= 1 1 0 0 30 0 1 0 0 O 0 1 0 O O 0 1 T5= 1 0 0 20 0 1 0 0 O 0 1 0 O O 0 1 If we multiply all these matrices we get T= Toffee' x T' x T2 x T3 x T4 x T5 T= O O I O 0.7071 -0.7071 0 60.1041 0.7071 0.7071 0 60.1041 O O 0 1 -lo From this last matrix we can see where the end-effector is and what its orientation is. The first three elements of the last column (0, 60.1041, 60.1041) tell us where it is with respect to the origin (the palm). It's O units in X, 60.1041 units in Y. and 60.1041 units in Z. The first three elements of the first through third columns are the unit vectors of the last reference frame with respect to the origin. As the variables change (the in each joint) the thumb is moving and the entire matrices have to be re- evaluated to calculate the new position and orientation References [1] P. Lopez and J.N. Foulc. "Introduction to Robotics volume I ", Glentop, 1986 [2] R.S. Hartenberg and J. Denavit, "A kinematic notation for lower pair mechanisms based on matrices", Journal of Applied Mechanics, vol. 77, pp. 215-221, June 1955.

[3] P.I. Corke, "A Robotics Toolbox for Matlab", IEEE Robotics and Automation Magazine, vol. 3, pp. 24-32, March 1996.

Claims

1. An artificial hand which has, inter alla, (a) a frame portion defining a base Cartesian coordinate reference frame; and (b) an artificial thumb, being a thumb which comprises: (i) a metacarpal phalange part; (ii) a medial phalange part; (iii) a distal phalange part; (iv) a two-degree-of-rotational freedom joint coupling said metacarpal phalange part at one end thereof to said frame portion with one of the rotational axes of the rotary part of said joint offset angularly with reference to said base coordinate reference frame; (v) coupling said metacarpal phalange part at the other end thereof to one end of said medial phalange part, a universal joint; and, (vi) coupling said medial phalange part, at the other end thereof, to said distal phalange part at one end thereof, a single-degree-of- rotational freedom joint.

2. An artificial hand as claimed in claim 1 in which: said two-degree-ofrotational freedom joint comprises two single-degree-of-rotational freedom portions the portion having its rotational axis offset angularly with reference to the base coordinate reference frame, and the other portion having its rotational axis orthogonal to the rotational axis of said first portion.

3. An artificial hand substantially as hereinbefore described with reference to the accompanying drawing.