Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

doi:10.1007/s11465-019-0570-x

Front. Mech. Eng.

2020, Vol. 15

Issue (1) : 66-80 https://doi.org/10.1007/s11465-019-0570-x

RESEARCH ARTICLE

Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

Xiaodong JIN^1,², Yuefa FANG¹(

), Dan ZHANG²(

), Xueling LUO²

¹. Department of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, China
². Department of Mechanical Engineering, Lassonde School of Engineering, York University, Toronto M3J 1P3, Canada

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Abstract

The parallel spindle heads with high rotational capability are demanded in the area of multi-axis machine tools and 3D printers. This paper focuses on designing a class of 2R1T (R: Rotation; T: Translation) parallel spindle heads and the corresponding collaborative 5-axis manipulators with 2-dimension (2D) large rotational angles. In order to construct 2D rotational degrees of freedom (DOFs), a platform with 2D revolute joints is proposed first. Based on the constraint screw theory, the feasible limbs that can be connected in the platform are synthesized. In order to provide constant rotational axis for the platform, a class of redundant limbs are designed. A class of redundant 2R1T parallel spindle heads is obtained by connecting the redundant limbs with the platform and the redundant characteristics are verified by the modified Grübler-Kutzbach criterion. The corresponding 5-axis collaborative manipulators are presented by constructing a 2-DOF series translational bottom moving platform. The inverse kinematics and the orientation workspace as well as the decoupling characteristics of this type of 2R1T parallel spindle heads are analyzed. The results show that these manipulators have large 2D rotational angles than the traditional A3/Z3 heads and can be potentially used in the application of multi-axis machine tools and the 3D printers.

Keywords parallel mechanism redundant mechanism large rotational angles machine tools 2R1T spindle head collaborative manipulator

Corresponding Author(s): Yuefa FANG,Dan ZHANG

Just Accepted Date: 11 December 2019 Online First Date: 27 December 2019 Issue Date: 21 February 2020

Cite this article:

Xiaodong JIN,Yuefa FANG,Dan ZHANG, et al. Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles[J]. Front. Mech. Eng., 2020, 15(1): 66-80.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0570-x
https://academic.hep.com.cn/fme/EN/Y2020/V15/I1/66

Fig.1 Processing models: (a) 3-dimension translational 3D printing process; (b) wedge- and (c) arc-shaped workpiece.

Fig.2 Synthesis procedure flow.

Fig.3 [PLA] with 2D rotational axes. Subscripts F and C represent force and couple, respectively.

Fig.4 An example structure 3???-[PLA] that satisfies the constraint condition.

Fig.5 2R1T spindle heads’ default view and side view: (a) 4???-[PLA] head; (b) 4P??-[PLA] head; (c) 4?P?-[PLA] head.

Fig.6 Constraints analysis of (a) limb 3; (b) limb 1 and the configuration that the platform rotates about v first.

Fig.7 The limb 1 and the configuration that the platform rotates about u first.

Fig.8 The part lists and exploded pictures and the assembly drawing of the bottom collaborative platform.

Fig.9 The 5-axis collaborative manipulators: (a)

4 R ˙ R ˙ R ˙ − [P L A] − [P ˙ P ¨]

; (b)

4 P R ˙ R ˙ − [P L A] − [P ˙ P ¨]

; (c)

4 R ˙ P R ˙ − [P L A] − [P ˙ P ¨]

Fig.10 Geometrical model of the 4P??-[PLA] spindle head. (a) The whole structure; (b) joins Q₂ and Q₃; (c) joins A.

Parameter	Value	Parameter	value
$l O B$ , $l O C$ , $l O D$	60 mm	$l A Q 1 y$	20 mm
$l A B$	30 mm	$l A Q 1 z$	30 mm
$l Q 2 C$ , $l Q 3 C$	30 mm	$P 1 b$	(–100, –20, q₁)
$l A Q 4 y$	20 mm	$P 2 b$	(0, –100, q₂)
$l A Q 4 z$	15 mm	$P 3 b$	(0, 100, q₃)
$l P i Q i$	150 mm	$P 4 b$	(–100, 20, q₄)

Tab.1 Architecture parameters of 4P??-[PLA] head

Fig.11 Geometrical projections of limb 1 in X_bZ_b-plane: (a) 4???-[PLA] head; (b) 4P??-[PLA] head; (c) 4?P?-[PLA] head.

Spindle head	l_OB/mm	l_AB/mm	$l A Q 1$ /mm	$l A Q 4$ /mm	$l P i Q i$ /mm	$l O i P i$ /mm	$l O i O b$ /mm
4???-[PLA]	60	30	30	15	150	90	150
4P??-[PLA]	60	30	30	15	150	–	–
4?P?-[PLA]	60	30	30	15	–	–	100

Tab.2 Architecture parameters of limb 1 in X_bZ_b-plane

Fig.12 Values of q₁ and q₄ to maintain joint A horizontal: (a) 4???-[PLA] head; (b) 4P??-[PLA] head; (c) 4?P?-[PLA] head.

Fig.13 1-dimension rotation capabilities along z axis: (a)

β = 0 ∘

; (b)

α = 0 ∘

Fig.14 The example rotational configurations about (a) x-direction by 90°, (b) y-direction by 90°, (c) x-direction by 45° and y-direction by –45°, (d) x-direction by –90°, (e) y-direction by –90°, and (f) x-direction by –45° and y-direction by 45°.

Fig.15 The orientation workspace at the position of (a) z =–240 mm, (b) z =–180 mm, (c) z =–120 mm, and (d) z =–60 mm.

Fig.16 Relationships between rotational angles and input parameters: (a) a and (q₁, q₂, q₃, q₄); (b) b and (q₁, q₂, q₃, q₄).

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